Here's the song classic "Baby It's Cold Outside" done not once but twice with some nice physical comedy elements. Both are from the 1949 movie Neptune's Daughter, for which it won the Best Song Oscar. The first version features Ricardo Montalban trying to seduce Esther Williams. The second version reverses the roles, with Betty Garrett putting the moves on none other than Red Skelton (Spanish accent and all).
I don't see a choreographer listed on the IMDB page, but director Edward Buzzell had acted in Vitaphone shorts and in a couple of Marx Brothers movies, so I suspect he gets at least some of the credit.
Side note: Betty Garrett and her husband were on the Hollywood Blacklist during the McCarthy era for refusing to name names to the House UnAmerican Activities Committee, but later toured with their own duo act.
Thanks to Riley Kellogg for the link!