It isn't the frequent bathing that causes dry skin. You can use a very mild shampoo (I use the #1 All systems Super Cleaning & Conditioning Shampoo)
http://mjmcompany.com/1allsystems-grooming.htm
This shampoo is for sensitive skin, fragile coats, puppies, kittens, residue free and safe enough to use every day.
You will need to give Omega fatty acids in the puppys food. I use cod liver oil. You can also use fish oil.