There will be doctors that will sign that they 'gave' you the vaccine but throw it away. Yes. They will be hard to find. Word of mouth. But they will exist.

I am certainly going to 'get' the vaccine, but will not inject anything into my body.

Traditionally you could go to a CVS, and 'buy' a Flu Vaccine, and the second you have the receipt walk out with your proof of purchase. This is what my wife does for her work which requires a flu vaccine to work there.

Gonna need to figure out how to be listed as being vaccinated without actually getting it.