You can even shave with hand cream. They suggest this for men if they have forgotten their shaving cream and are at a hotel -- hand cream is closer in formulation to shaving cream than shampoo is, and so it's the suggested substitute.
Another out-of-the-expected remedy for itchy skin (especially insect bites, but it might work here too) is classic formula Listerine. It has all sorts of ingredients in it that are soothing to the skin and kill the itch.
If it's not the hypoallergenic thing, you might try some moisturizing shaving cream. My legs get dry and itchy if I use regular shaving cream or fail to put lotion on if I do use regular shaving cream.
Change the cream if your are using try something else and see.
It might be the products you are using; try an hypoallergenic body wash.