Man - that's a good question.

Not sure about on the beach, but in town try Skipper's Barber Shop on Beck Ave. It's been years since I've been there, but those guys do the lather shave w/ a straight razor, etc.
Skipper's Barber & Beauty Shop

Also - this came up in a Google search... might be worth a try... right by the mall in town:
Panama City Barber Shop

Not sure about about barbers on the beach... but there is one right across the street from the Navy base on Thomas Drive that looks like it would be worth checking out. Can't remember the name, though...