I found out the name of the puppeteer in Santa Claus’ Punch and Judy – George Prentice, a Punch puppeteer mentioned in Bill Baird’s classic book The Art of the Puppet. The film is available for sale from Puppetstuff as part of a VHS holiday compilation called The Night Before Christmas that also includes another classic Christmas puppet film, The First Christmas.

Thanks to Dusty Teague for the tip!