A tip of the hat to The Wonderful World of Louis Armstrong blog and its creator, Ricky Riccardi, for researching the history of Satchmo's recording and the evolution of this tune. Be sure to check out his book, too.
Craig Klein's rendition is faithful to the tradition, presenting the minor-key section as a bluesy dirge, and picking up the second-line tempo of the major-key section in order to send 'em home. The pairing of major and minor tonalities is similar to other traditional tunes like "St. Louis Blues," as well as modern songwriting techniques that use a minor verse into a major chorus.
Klein's trombone solo even shifts tonalities as the band swings, from major to minor pentatonics, as if playing around in the major scale requires finesse while the minor allows you to let loose. Klein's playing is never out of control, every note has a purpose, but there seems to be a shift in focus from running down the scale to punching you in the gut. Especially in the tag at the end of the tune, the use of accenting the up-beats of three and four is an effective way to add rhythmical energy to the performance.
Here is a YouTube video of Swedish trombonist, Karel Eriksson, performing this tune. Is there anything the Swedes can't do?
Recommended reading: What a Wonderful World: The Magic of Louis Armstrong's Later Years by Ricky Riccardi. Published by Pantheon.