NY State is following CDC guidance. The CDC has advised that vaccinated individuals no longer need to wear a mask or physically distance. Therefore, vaccinated individuals are permitted in exam rooms without masks and without physical distancing. However, unvaccinated individuals must wear masks in public settings, and the Department of Health strongly recommends masks in indoor settings where the vaccination status is unknown or where the individual is unvaccinated. This means all businesses are required to maintain 6 feet of social distancing unless all individuals are vaccinated.
Therefore you cannot admit a vaccinated client to an examination room if an un-vaccinated individual is present, unless that room allows for 6 feet of social distancing.
If you can keep the client 6 feet away from an un-vaccinated employee, you should follow the Department of Health recommendations and require the un-vaccinated employee (but not those who are vaccinated) to wear a mask.
You cannot mitigate the risk by asking the un-vaccinated employee to sign a waiver to relieve you of responsibility for their safety, just as you cannot allow an employee to do anything else unsafe on your property.