Here’s another interesting YouTube find: George E. Lee and his Novelty Singing Orchestra, doing “SJI” in a 1929 recording. Like the previously noted White Stripes “video” version, this one is just the song plus a sort of montage of images, mostly taken, I assume, from around the Web. (The image of the sheet music is actually from this site, I’m pretty sure. Which is fine with me. I’m just noting it.)
In the comments to the YouTube video, there’s an interesting observation to the effect that Cab Calloway’s interpretation of “SJI” owes quite a bit to Lee’s. And while I’d never thought of that before, listening now, I see the commenter’s point.