One of the songs they do is a Bob Wills song. One of the few songs we've found that both I know and they know is Cocaine Blues, which I learned from albums by George Thorogood and Johnny Cash, but they told me that Jimmie Rodgers did it first.

I understand about Hank not singing about cowboys, but the instrumentation and vocalizing in his songs puts me in mind the of movie star cowboy singers (not the best references, I realize).

okay, here's more worms. What defines what genre a song goes into? I've got the song "Busted" as recorded by a number of different artists. The lyrics are about living on a farm and having no money. Nazareth recorded it as a slow shuffle blues with lots of single string guitar work. Johnny Cash's version is in 6-8 with that prominent 1-2-3, 1-2-3 that makes me think of horses. John Conlee does it in 4/4 with a 1-5-1-5 bass line and a twang in his voice, giving it a modern country feel.
So is it the lyrical content, or the style of music that defines it?

The reason I'm asking this is because I'm a blues guy and I will get bored silly doing a basic 1-5-1-5 all the time. At the very least I'd like to throw in a few pickup notes and walk ups/downs for chord changes. I'd really like to do some walking bass lines, but I don't want to start alienating the audience(s) either. If the genres are that blended, will that be such a danger?

Or is this something I just need to keep an eye on the audience to see how they respond? (Which will be hard because at the 2 gigs we've done so far I've had to keep my eyes riveted on the rhythm guitarist's hand to see the chord changes since I didn't know any of the songs). I tried asking the band about how to play it, and they said "Do whatever you want." I think because their original bassist didn't know how to play (literally - he was learning the basics off a video tape).