I posted this here not long ago. From the published script: "At a certain point in the number, Bill comes out for a quiet smoke, tosses cigarette away, and joins Paul and his two friends in a spirited jazz session into which the dancers throw themselves with Bacchanalian zest. We must assume that it's never too hot to dance."
Yes, there are several things in KMK that make no sense. You either accept them or you don't. I have a lot more trouble with the question of what is going on onstage in the Shrew musical when all four of the principals seem to be offstage for very long periods of time.