I'm not questioning your method of handling the confrontation, however, your medical exemption is your affair and is therefore your private business.
I've done that, and it annoyed me thinking I have to offer an excuse or a reason to refuse to accede to their weaponized hypochondria. Now, I'll just say NO and walk away.
I agree. I shouldn't have to give a reason. And on occasion I just ignore.
I actually had a woman run from me one day while shopping saying NO Mask! And she stayed away from me lurking around the corner until I moved to another aisle.
But note I didn't say *I* had an exemption.
One time the guy at the door a Sam's club stopped me and I asked "You accept medical exceptions?" He said "Oh, yes go ahead." I just asked a question.