When I have pet-sat for my bosses' animals, Willie, the kitty, is always desperate to be petted, and I am horribly allergic to him. What I did one day was pick up a thick paper towel, and petted him with that. We were both happier that way. I still washed my hands immediately after discarding the towel, but I don't get as wheezy/itchy.

I'd clean their cages outside if possible, and always wear gloves - rubber gloves or even gardn gloves - when ceaning their area, or even when petting them. You won;t get to feel their soft fur against your skin, but you won't suffer the aftermath, either.

Do you take any antihistamine regularly?