I don't know where TV.com gets its information, but there was no Christmas shopping television episode aired on this date. I've read the actual script for the show that aired that day, and it's not about Christmas shopping. It's an episode where Jack goes grocery shopping. Mel Blanc isn't even in it.
For proof of this, go to http://www.tobaccodocuments.org and do a search for Jack Benny. There you will find authentic scanned copies for every radio and television script Jack performed for Lucky Strike. These are official primary source documents that prove what aired on a particular date. There was no Christmas shopping episode done by Jack Benny on this date. In fact, the annual Christmas shopping radio episode aired the week prior.
The first televised Christmas shopping episode wasn't until 1957, and it's never been released on video or DVD. The version that everybody has seen is the 1960 version, regardless of the date on the package.