This caused some consternation. We wondered whether Cheek to Cheek was a suitable tune for a traditional jazz band. It's trickier than standard 32-bar songs, because it runs to 72 bars and the structure is A-A-B-C-A. (Part C is just 8 bars, mainly using minor and diminished chords.)
We also thought just three choruses would be quite enough. We played two ensemble, with our clarinet player providing a pretty good vocal between them. It turned out reasonably well, but I think it would be foolhardy for anyone (in our band at least) to attempt a full improvised chorus over the 72 bars.
The book Playing Traditional Jazz by Pops Coffee is available from Amazon.