My son has worn a ball cap, a nice pair of khaki shorts, and a collared shirt. I believe this is the best policy. Obviously, some could get away with less, but why take that chance? For one, even if it didn't matter, shouldn't you show your son to have a little more respect for the staff and the situation at hand? It is a big deal, and he should treat it as such.
If there is a work out after the tour, he can obviously bring a bag with other clothes. Dress comfortable, and fit in. Wearing a nice pair of khakis, ball cap, and a collared shirt will let you fit in pretty much anywhere.