The rules issued by the Occupational Safety and Health Administration require private-sector employers with 100 or more workers to ensure their employees get fully vaccinated or take a weekly Covid-19 test and wear a mask at work. OSHA can issue fines against companies for noncompliance. The OSHA emergency temporary standard can stay in place for six months before it would need to be codified as a permanent standard that requires rule making.

The Fifth U.S. Circuit Court of Appeals in New Orleans earlier this month granted an emergency stay prohibiting enforcement of the rules for now, saying they raised “grave statutory and constitutional issues.” The Sixth U.S. Circuit Court of Appeals in Cincinnati was randomly selected on Nov. 17 to take on legal challenges to the mandate, and on Tuesday the Biden administration filed an emergency court motion seeking the immediate reinstatement of the mandate.

Around 50% of organizations surveyed by the Society for Human Resource Management say uncertainty around the legal challenges to vaccine mandates is presenting challenges to their implementation. “The rest are actually preparing for compliance,” said

Emily Dickens,

SHRM’s chief of staff, head of government affairs and corporate secretary.

Many businesses already were in the process of implementing different types of vaccine requirements before the emergency temporary standard, or ETS, was issued, and the emergence of the Delta variant may have further accelerated moves in that direction, said Kevin Troutman, an attorney at Fisher Phillips and a member of the law firm’s Covid-19 task force.

“But certainly [when] the president’s announcement…was released, people were again trying to do everything they could do to understand the requirements and start to implement them,” Mr. Troutman added.

Businesses are confronting a number of implementation issues, experts say. Companies, for instance, have to decide how to record and submit compliance with the mandate, and determine whether they should strictly require employees to vaccinate against Covid-19, or allow workers who are resistant to vaccines to test weekly and mask up at work.

Additionally, despite a provision in the mandate that says employers aren’t required to provide or pay for tests, businesses must decide if they should shoulder the costs to help retain employees.

“Certainly at this point where we sit today, before we’re too close to the January vaccination deadline…you should be doing all of the back-office things that you are going to need to do to be in compliance,” said Brett Coburn, a partner at the law firm Alston & Bird focused on employment litigation and counseling.

Keeping an eye on the appeals process is important, however. “I wouldn’t make a big financial commitment in terms of testing or anything else until we know what’s going to happen,” said Mr. Coburn.

How a company’s implementation rolls out will depend on its size, said Helene Hechtkopf, a partner at the law firm Hoguet Newman Regal & Kenney LLP focusing on employment and commercial litigation.

“I have heard of companies bringing in someone to do the testing once a week. But if you have 100 employees, and you have three unvaccinated employees, that doesn’t make any sense,” Ms. Hechtkopf said.

A web of state and local laws further muddies the waters. Although federal law takes precedence over state laws, it is crucial for businesses to know what other issues they may face in jurisdictions where they operate.

This is especially true when it comes to who will pay for weekly testing, SHRM’s Ms. Dickens said, adding that some cities and states already have their own mandates, and about one-third of businesses the organization surveyed already are planning to cover testing expenses.

“And remember for Covid tests, insurance may cover the costs, but there are several laws predating Covid requiring employers to pay for mandatory medical tests, or to reimburse their employees for such testing,” said Ms. Dickens.

Industry experts emphasize the need for communication between employers and their staff, given the resistance to mandates among many and the lack of clarity about the legal challenges that lie ahead.

“On the one side of the spectrum, you can say nothing and you can just be quiet and wait and see how things play out in court,” said Mr. Coburn. “On the other side of that spectrum, you could say, ‘Well we don’t care what the courts say, we’re going to implement an ETS-compliant policy’…The middle point is to have some communication with your employees, but to just take head-on the fact that there is uncertainty.”

The bottom line is companies should prepare for all scenarios, experts say.

“I think some companies have decided to tap the brakes a little and just see how this was all going to work out,” said Mr. Troutman. “But we’ve certainly recommended that you, at least as an employer, continue to be prepared. And that means, at least where you’re able to, assess…who’s vaccinated and who’s not in your workplace…If you don’t do that much, at least, and let’s say that the ETS moves forward on or close to the current schedule, you’d really be behind the eight ball.”

Write to David Smagalla at david.smagalla@wsj.com