There are, of course, lots of good choices of more natural products available at Holistic Pet Stores. The breed of dog, size of dog and any skin conditions will be determining factors in your choice of product. I have successfully used blue Dawn on my Bichon and it did an excellent whitening job. I did not use it often to avoid drying his skin, as would be the case with any shampoo.
Dawn is, after all, what they use on wildlife caught in oil spills.

It is always good to check with the vet. Slippery elm is an excellent herbal treatment as well. It is considered safe and can be added to the dog's food for ease in administration. Do your homework and look it up on holistic veterinary websites.