From the Library of Congress's "National Jukebox" database:

Recording Title: Hesitation blues
Musical group: Victor Military Band
Composer: Billy Smythe
Conductor: Edward T. King
Genre(s): Ragtime, jazz, and more, Blues
Category: Instrumental
Description: Band
Label Name/Number: Victor 18163
Matrix Number/Take Number: B-18339/3
Recording Date: 1916-09-15
Place of Recording: Camden, New Jersey
Size: 10"
Duration: 03:02
Notes: Victor ledgers note: 15 extra men.

I've played the recording and the main theme is very clearly the original of the "Hesitation Blues" song. It seems to me that this composition is the original tune and, like others before it, it's passed into blues folklore. The Victor Military Band was composed of black musicians, which may or may not have been a factor in the tune being adopted by the early blues men.