The strange sights and smells and even the carrier and car ride can really upset cats alot more then it does dogs. There are vet that make house calls, look in the Yellow Pages and see what you can find. If you can not find any, the call your regular vet and see if he/she will make a housecall for an extra charge.
BUT, if your cat does not go outside, you have no other pets that go out, then you are pretty safe in skipping a few years between visits.
Even if the vet comes to your house, he/she will carry smells that will upset your cat. Your best bet is to take the cat, warn the staff and they will make arrangments to deal with it. They are trained for these situations and know how to deal with it without putting themselves, you, and your cat in danger.
Hope this helps.
The only vets I have heard of in Western NY who make house calls are farm vets. Never heard of a bird vet who made house calls. You pay through the nose for house calls.