Want to adopt but SO gets hives

Recently my SO and I have looked into adopting a cat. We both fell in love with one at a no-kill shelter nearby, but unfortunately my SO begun experiencing hives an hour after handling it.

We think it's either a general dander allergy OR an allergy to anything the cat's fur may be treated with. Unfortunately we can't adopt with this condition, and we can't really afford $800 immunity shots. Would just taking a Zyrtec every day work until my SO is accustomed to it? They used to have a cat they weren't allergic to.