Hi, Tim, I'd sugggest having a word with your doctor as there are
desensitising treatments available now for many allergies. What needs to be
ascertained is whether your allergy is to fur, dander or saliva. Is it just
cats you're allergic to or other animals as well?

Otherwise, there is a product called Petal Cleanse which can be applied to a
cat's coat. And some people find that cats with less fur, such as Devon or
Cornish Rex, can be tolerated.