I have heard the following: Only use soap/shampoo on your cat that is made exclusively for cats. Using other products can irritate their skin, make them sick and sometimes even kill them. Even using dog shampoo on a cat can kill the cat.
I would see if there is a similar type of product for cats. Call your vet and ask if they recommend any special cat shampoo. I'm sure there is something out there. I saw on a website recently that if you wash your cat in luke warm water only once a week, no soap or shampoo needed, that it will help with cat owners who have cat allergies. It also said to wash the cat's bedding in warm water once a week as well, no soaps.
Good luck!!!