While not technically OTR, this is an audio comedy from the same era and by a famous OTR actor. Stan Freberg was known for doing parody skits. In this case, it’s a parody of Dragnet, but with the “crime” being that of not believing in Santa. This skit also features the voice of Daws Butler (who did most of the voices in old Hanna-Barbera cartoons).
Here’s a second holiday skit by Freberg, “Green Chri$tma$”, a skit about Christmas being too commercial. It also includes parodies of several classic Christmas carols.