Some info might help get good help back to you. Are you shooting in BW or color? What format? Beyond "a 1940's radio studio", you seeking a particular "look", i.e. high key, low key top light bottom light?
If they insist on hats, you might want to have them "illuminated" by a mixing board. Not really, but have them at a console of some sort and bring the light up from below so the hats don't kill the whole thing. Could be a low key moody shot. Yes, people will tell you light from below is macabre, and thus abhorrent, but it's not so macabre when it looks like it's just light from a source below the face - like a mixing board... Just a thought.
One more thought, can you do a test ot two, until you have a proven plan or two, with a couple of folks who are just there to model for test shoots?
Best,
C