Very cool. I’m a big Electro Swing fan, this sounds like an interesting thing to get involved in.
Obviously there’s the (always copyright-problematic) route of digging out old samples. I’d say with some chopping and beatgridding you could quite quickly build a library of different swing beats you could lay over the top of live musicians. On top of that a library of retro vocal samples would be useful, plus things like piano stabs and short loops. Depends how crazy you want to go really. Plus, if you bought some cheap midi drum triggers you could even play along with some basic beats (or add some bells and whistles).
If I were you I’d go along to a rehearsal and see what they want, dig out a few simple loops you can drop in and see how it sounds… and let us know how you get on! I’d love to be involved in something like this one day so be interested to see how you go!