With a puppy you just want to hold him on your lap and run the comb through his fur. Keep him as comfortable as possible. Even with a short cut you pup needs to be used to being handled and touched on a regular basis so he will continue to be good for the groomer.
I give Gracie a weekly bath but we use an all natural shampoo and conditioner. Many of the brands you see in department stores and pet stores use sulfates that do strip the skin and coat. I use Yorkie Splash and Shine but there are other products out there that are all natural as well.
Yorkie Splash and Yorkie Shine | Yorkie Shampoo and Yorkie Conditioner