Business leaders broadly agree they need to get more workers vaccinated to keep the U.S. economy humming in the face of the fast-spreading Delta variant.

But they’re split over how best to do that. Some are dangling bigger bonuses or other incentives to cajole employees into getting the Covid-19 vaccine. Others have started requiring workers get the shot.

In recent days, companies from Arkansas-based Walmart Inc. to Microsoft Corp. in Seattle have imposed vaccine mandates mostly on white-collar workers returning to offices. Meatpacker Tyson Foods Inc. on Tuesday took a harder line, saying all its workers must get the vaccine by Nov. 1.

“We did not take this decision lightly,” Donnie King, Tyson’s chief executive, wrote in a memo to the company’s roughly 120,000 U.S. employees. “We have spent months encouraging our team members to get vaccinated—today, under half of our team members are.”

Both strategies come with risks for employers, their workers and their customers, and both could shape the course of the pandemic.

More than a third of American adults have not gotten vaccinated, according to the latest U.S. data. Firms using a lighter touch risk workplace outbreaks. Those mandating shots risk losing workers in a tight job market.

Each CEO cites myriad reasons for their vaccine strategy, though many also point to new Centers for Disease Control and Prevention guidelines relating to how vaccinated people transmit the Delta variant.

Some companies want to reassure the public it is still safe to shop in their stores or visit their theme parks. Others want to prevent worker illnesses or absences from crippling their operations again. Still others want to end remote work and get staff back into offices. Union rules for a number of companies are complicating matters further.

Walmart executives didn’t make the Covid-19 vaccine mandatory this spring in part because executives worried it wasn’t readily available to all who wanted it and wasn’t yet fully FDA approved, said a person familiar with the situation. Last week, Walmart said it would require vaccines for U.S. corporate staff and regional managers. It isn’t mandating the shots for store workers.

Walmart’s vaccination rate is slightly higher than the national average, according to people familiar with the matter. However, with 1.6 million U.S. employees, that means hundreds of thousands of cashiers, truck drivers, warehouse loaders and other frontline staff likely have not gotten the vaccine.

A worker wearing a protective mask pulls shopping carts outside a Walmart store in Duarte, California. Walmart says it will require vaccines for U.S. corporate staff and regional managers.

Photo: David Swanson/Bloomberg News

Executives felt starting with corporate and regional managers—a small percentage of its workforce—would be easiest because many are concentrated in a few geographic areas and most are planning to return to offices in coming weeks, said a person familiar with the plan.

A Walmart spokesman said the company hopes that by asking executives to be vaccinated, they will “influence even more of our frontline associates to become vaccinated.”

In a tight job market for hourly workers, Walmart is competing for employees with Amazon.com Inc. and others that aren’t mandating the vaccine. Walmart is offering a $150 bonus to employees who get the shot.

Some U.S. airlines are requiring vaccines for new hires but not existing staff. Manufacturing giants such as General Electric Co. , Caterpillar Inc. and the big three U.S. automakers have said they aren’t mandating vaccines.

Snap-on Inc., a Wisconsin-based high-end tools manufacturer with a largely blue-collar workforce, won’t mandate the vaccine, says Chief Executive Nicholas T. Pinchuk, because he believes such a move would backfire.

“I don’t think the way to do it is to tell people, somehow because they don’t get the vaccine, they are flawed,” Mr. Pinchuk said. “They don’t respond to that.”

Outside the New York Stock Exchange this summer. Companies have begun to impose vaccine mandates, mostly on white-collar workers returning to offices

Photo: Michael Nagle/Bloomberg News

He instead talks up the benefits of the vaccine. The company has offered employees time off to get the shot. Snap-on’s overall vaccination rate is above the national average, said Mr. Pinchuk, with more factory workers than corporate staff having received the vaccine. He declined to provide specific figures.

Companies mandating vaccinations for workers represented by labor unions, such as Tyson, must negotiate those requirements. About 36,000 Tyson employees, or a quarter of its workforce, are unionized or covered by collective bargaining agreements.

Labor union leaders have sent mixed messages on vaccine requirements. Some have insisted such changes be reached only through collective bargaining, while others have come out publicly in support.

General Motors Co. and its rivals decided Tuesday to reinstate mask wearing across their workforces after discussions with a joint task force of the United Auto Workers union.

A UAW spokesman said a vaccine mandate would be subject to negotiations with union officials. He said the union has encouraged workers to get vaccinated.

After Walt Disney Co. announced last week it will require corporate and non-union hourly employees to be vaccinated, some unions representing Disney workers said they were largely supportive of the move.

Eric Clinton, president of a union representing about 8,000 ride operators, custodians and other workers at Walt Disney World in Orlando, Fla., said the mandates are a logical step to help keep employees safe. The union is meeting with Disney to bargain over the details of the mandate and how it could be implemented, Mr. Clinton said.

Workers at Disneyland in California wave to guests. Walt Disney Co. will require corporate and non-union hourly employees to be vaccinated

Photo: Christian Thompson/Disneyland Resort/Getty Images

Many food processing and retail workers are concerned about getting the vaccine for health reasons or because they distrust the government or are skeptical about the pandemic itself, said Stuart Appelbaum, president of the Retail Wholesale and Department Store Union, which represents workers in poultry-processing plants run by Tyson, as well as other companies.

U.S. employers can require all workers physically present in a workplace be vaccinated against Covid-19, the Equal Employment Opportunity Commission said earlier this year.

Most companies say they will allow for health and religious exemptions, and some are still determining how they will respond to workers who do not comply. One hospital system in Texas that required vaccinations as a condition of employment earlier this year fired some employees who refused to get vaccinated.

A Tyson spokesman said the company will continue to educate its employees about vaccinations, address their concerns, and will consider requests for exemptions on medical and religious grounds, but that vaccinations are a condition of employment.

Some executives expressed support for vaccine requirements early this year but few companies came forward with them until more recently, when public opinion on mandates began to shift, said Peter Cappelli, a management professor at the University of Pennsylvania’s Wharton School.

“Do you want to pick a fight at the very beginning with 100% of employees when the idea of vaccinating first comes out, or do you want to wait until the social pressure pushes almost everybody to do it, and then you’ve only got to lean on a small number of people?” Mr. Cappelli said. “It’s way, way easier to pull the trigger on a small minority than to try to force it on a majority of people.”

The move to mandate vaccines has happened fast. As recently as early last month, 15% of the roughly 150 employers that responded to a survey commissioned by law firm Blank Rome LLP said they would require vaccines, a figure that was about the same from the firm’s February survey.

Calls for vaccine mandates have also grown louder from some business and political leaders. In recent months, more hospital systems, universities and other organizations have adopted them and survived early legal challenges from employees.

“Everyone was trying initially to just respect everyone’s perspective around what they want to do [on vaccines], but we know that if we do that we could create a pretty serious situation,” said Francine Katsoudas, chief people officer at Cisco Systems Inc.

Cisco required that the limited number of employees working in its offices in July and August be fully vaccinated, guidance it expects to extend into the fall as offices reopen more broadly, Ms. Katsoudas said. “For a little bit, we have to control the environment,” she said.

Many companies already require drug tests, and some have mandated flu vaccines and other shots in the past.

Harvey Spevak, executive chairman and managing partner at gym operator Equinox Group, says discussions on whether to mandate vaccines became more urgent in the last ten days as cases ticked up and the CDC released new data and guidance on masking. Eighty-nine percent of Equinox’s employees who responded to an internal survey said they had received Covid-19 vaccines. The company employs about 14,000 people.

“We know this is a hotly contested issue, so it’s easier to be silent or Switzerland than take a position,” Mr. Spevak said. “With the surge in cases, this felt like the right thing to do.”

The company, which also owns cycling studio SoulCycle, will mandate vaccines for staff and customers in New York beginning in September, with plans to roll out the requirement to other locations. New York City announced Tuesday that people there will need to show proof of vaccination for indoor activities such as dining, gyms and events.

At steelmaker Cleveland-Cliffs Inc., CEO Lourenco Goncalves started an incentive program at the start of July with the goal of getting at least 75% of the roughly 25,000 employees vaccinated. Workers will receive $1,500 bonuses if at least 75% of the employees at their work sites receive the vaccine. For sites where at least 85% of coworkers receive the vaccine, the bonus increases to $3,000. The program runs through Aug. 21.

As the Delta variant sweeps the globe, scientists are learning more about why new versions of the coronavirus spread faster, and what this could mean for vaccine efforts. The spike protein, which gives the virus its unmistakable shape, may hold the key. Illustration: Nick Collingwood/WSJ The Wall Street Journal Interactive Edition

So far, just under 50% of all employees have been vaccinated, up from 35% when the program started last month. At the company’s Cleveland headquarters, 97% of the employees have been vaccinated, said Mr. Goncalves. At one of the company’s mills, in Conshohocken, Pa., 61% of the employees are now vaccinated, up from 20% when the program started.

Mr. Goncalves said he isn’t mandating the vaccine because he doesn’t need every employee to get a vaccination to reach a level that will lower chances of outbreaks at worksites.

—Jacob Bunge and Mike Colias contributed to this article

Write to Chip Cutter at chip.cutter@wsj.com, Sarah Nassauer at sarah.nassauer@wsj.com and Bob Tita at robert.tita@wsj.com