Hmm, this was done years ago. (Score 2, Interesting)

Breeders already have cats that are missing the allergen causing protein from their saliva.

Bengal Cats and Siberian-Russians are two such breeds, and several unofficial subbreeds also fit the bill.

Google if you want breed info, but Bengals are a short haired, very outgoing breed with great social skills and tons of energy. The also play fetch and are suprisingly clever. Siberian-Russians are a long haired breed who behave more like traditional cats, in that they can be fat and lazy all the way through to hyper.