In my personal opinion, a vet trip would be an absolute overkill.
When I started out and had my BPs in glass enclosures, I had some horrible sheds. Usually upping the humidity and throwing in some sphagnum moss would do the trick. In regards to soaking, don't do it! You're just washing out the natural oil that they use to shed. Let them do their own thing. Leave some damp moss around his enclosure and let him do his own thing.