They make puppy shampoo, so you could try that on him. I bathe both of mine every other week. I use to bathe Izzy weekly, but now with 2 of them, it's just too much. I know a lot of people will say that every week, or every other week is too much, but they have beautiful coats, and do not have dry skin whatsoever. I bathe them in the bathtub, and have one of those sprayer shower heads that have a hose 6 feet long. That makes it A LOT easier to bathe them with that, and I get all the shampoo off of them. I use special shampoo from the vet that smells wonderful!!! When Izzy was a baby, she would get these itchy bumps all over her. They thought she was allergic to something (still haven't figured out what), but as long as I give her a bath with this shampoo, she doesn't have the itchy bumps. If I don't bathe her, she starts to get them again. I am thinking she is allergic to something in the house, like I am. Then when Gus came along, I just started using the same shampoo on him. Just make sure the water is nice and warm.... mine don't like it cold, they will shiver if it's too cold. I use a wash cloth to clean their face off. They don't really like the bath, but they LOVE getting dried off!!!!! I dry them with a big towel first and they stand still, perfectly. Then, they know when I get the second towel out it's time to have FUN. They go crazy, and I let them play with that towel, and they run around like crazy butts!!! Then, they are nice and tired after they are done being crazy.
Good luck with your puppy! I would start right away giving baths to get him use to it.