This video is such fun because he seems to be having a great time, and the audience is enthralled by it -- in large part because he has such a distinctive voice and he's able to hide it.
But that's not why this video is a pleasure. There's something else of which I shall say no more. But all of this together makes this such a joy.
This is the full episode -- the Mystery Guest segment begins at the 16-minute mark.
By the way, there's a bit of a P.S. to all of this.
(It's best not to read it until after you watch the video above, so as not to spoil the small surprise. But for thems what have got that far -- )
From what I've read about Louis Armstrong's appearance on the show, apparently he wasn't supposed to sing the song. He was making another TV appearance later that week and (supposedly) there was a condition of exclusivity, where he would only sing "Hello, Dolly" and when he began to sing, his manager went nuts.