When I saw this question I immediately said, "Dawn." I clicked the link to answer and see someone else has already answered the same. Dawn is what most people suggest and is safe to use on a young puppy. When my girl was young I was advised that even the puppy flea shampoo wasn't safe because they are for older pups I think around age 10 weeks+. That's just my guesstimate.
Like cobrien said it's safe enough to use on wildlife and it's what they use to clean all the oil spill covered birds.