The character of Vera Simpson sings "Zip!" in the film version of the show as well. I believe some lines were added to establish that she is a former stripper and, when she is asked to get up and do a number with the orchestra at a charity function, "Zip!" is what happens.
I imagine that something similar might have been done to allow Horne to sing the song, either because they may have thought that people expected it, due to the film, or maybe simply because Horne wanted to do it.