Indoor-only cats

Does everybody who has indoor-only cats still get them all their shots?

I just got a card saying that Koala will be due for an FVRC-P shot next
month. Neither of my cats even shows an interest in going outside, and
nobody ever brings animals here.

Koala has finally gotten to the point where he trusts me. I'd hate to
destroy that trust by catching him, sticking him in a carrier, and
taking him to the vet. Not only that, I'm not at all sure I could do
it. I'm closer to my 80th birthday than my 79th, and he's very strong.
He also has sharp claws, because I can't cut them. He will sit on my
lap, and he now loves to have me pet him, but I can't pick him up or
hold onto him.

Suggestions?

Joy