that's a tough issue.
Denying someone the right to work is basically denying them the right to life. I can definitely see a justification for requiring it among some professions (Medical, Law Enforcement, maybe Food Handlers..... Public Transit workers? Uber and Lyft Drivers?.) But your truck drivers and office workers and other more common job workers? Harder sell for a mandate.
There's the question, "Is Health Care a Right or a Privilege?"
The flip side is, "Can I force a medical treatment on someone who adamantly is opposed to it?"
Here's the really tough nut to crack: How are we expecting people to "prove" they have been vaccinated? People are already forging Covid Test certificates
Prosecutors say seven held at Charles de Gaulle airport tried to sell fake test certificates.
www.bbc.com
A tattoo would be the obvious answer, and would bring down the wrath of a LOT of people who would decline the vaccination possibly for that and only that reason. And for that matter, a tattoo could be faked. How about a "chip"? Now you're REALLY going to freak a non-negligible portion of the population out!
My gut feeling? Make it freely available to everyone on the planet. If they take it, fine. If they don't, 90% or more are going to GET Covid, most of whom are going to do fine, some of whom are going to have permanent sequelae, and some of whom are going to die. In the U.S., for the most part, people are free decline health care, with exceptions in schools, military, and Medicine.