The song: s_carolina_rag.mp3 (recorded from 78 rpm record to cassette, to computer).
I can't find the original recording details, but apparently it has been reissued on East Coast Blues, 1926-1935, Yazoo L-1013.
And here's an interloper: Big Bill Broonzy and Frank Brasswell playing Pig Meat Strut (MP3). This piece seems to be very much a duet in the original, with Brasswell's walking bass running throughout.