I heard some Russians have tried this but only in bulk as it turned more effective:

1. Get policy printed out and get a signature from employer that they ordered you to get a shot. (doubt any USA employer would sign it but its an idea),
2. go with this paperwork to the vaccination site and on the paperwork where your signature is required that you do it on your own volition - strike it out and write in that you are doing it at the order of such and such and putting all responsibility on such and such as in your work papers.
3. medic will REFUSE to give you vaccine under such circumstances.
4. You get it on paper that they have refused to vaccinate you.
5. You get back to your employer with paper that states refusal from medic to vaccinate you - they can't fire you because of non vaccination. However, they can come up with any other bogus reason to fire you anyway. Now, suing them for liability once employees get INJURED I predict will happen. It will be up to courts to decide whether it is employers fault or you actually did it on your own at your own volition since you are the one coming to vaccination site and signing non-liability papers. Also, I would not be surprised if local govts will pass non-liability laws soon for employers as it was just tried in CA and so far pushed for later.