C.W.
There are cat only clinics where I have lived. I have only worked in small animal or emergency clinics. With general office experience you could possibly work as a receptionist but your time with the actual cat would be limited except for hearing a screaming cat carrier walk by.
See if you can volunteer to actually learn proper handling...they don't want somebody without experience restraining the cat. Veterinarians and technicians don't like to get bit. Maybe as a kennel attendant cleaning cages in the morning.