I do think the atmosphere could be perfectly like a 1930s Barber shop from a Gangster movie. That would let you change the costume slightly to be 1930s if you wished.
There would be dull lighting, which you could break up by giving guests glow bracelets and sticks.
I think graduation party ideas do need the right guests. A barber chop is famous for people talking together, sharing the news and having fun.
Be sure you have the right guests for it.