The message from Jim reminded me that I enjoyed the video when I first saw it in 2012. At the time, I remember listening also (for comparison) to the original 1926 version composed by Lil Hardin Armstrong and recorded by Louis Armstrong's Hot Five (also available on YouTube).
But on that occasion, apart from feeling that it was a very good but quite complicated piece of music, I thought no more about it.
Jim enjoyed the performance and particularly praised Shaye's muted cornet work. Throughout the three minutes, Shaye uses her Humes and Berg 102 stonelined cup mute and has it fully wedged inside the bell of her cornet. We know that on other occasions, she prefers to hold it half in and half out of the bell. Barnabus also, using his Humes and Berg stonelined straight mute, plays some lovely stuff complementing Shaye's melodic lines. Jim also specially liked the final Chorus, in which Shaye and Barnabus play so well together, alternating the 'breaks'.
We must all be grateful to the video-maker codenamed jazzbo43 for recording this fine performance.
It's interesting to observe how Ryan (at 2 mins 08 secs) warns Max that the band is about to go to the 12-bar 'breaks interlude' rather than the start of the Chorus; and then (at 2 mins 24 secs) that this time they are returning to the start of the Chorus. (The 'Breaks Interlude' is copied from the original Armstrong recording.)
Perhaps Max hadn't played this number with the band before. (In fact it is a song they seem to have played very rarely over the years.)
After Jim encouraged me to listen more carefully to it again, I realised Droppin' Shucks is not really as complicated as I had thought. Basically it has a simple and pretty 16-bar minor-key Verse played once (Tuba Skinny play it in C minor); and then the Chorus - played several times (in the key of Ab) - is simply one of those 16-bar standards (with 'breaks' on Bars 9 - 12), very similar to How Come You Do Me Like You Do Do Do? or If It Don't Fit, Don't Force It or Don't Care Blues or Don't Go Away, Nobody, or Forget Me Not Blues.
The only little extra ingredient is that 12-bar 'Breaks Interlude' I mentioned - which may be regarded as optional.
So it's easy to pick up. Let's have more bands playing it!
As for what the title Droppin' Shucks means, I think you may be able to find out. But I shall say nothing on the subject. Regular readers will know that I limit the contents of my pages to the decorous, the refined, and the tasteful.