I'd be careful about the choice of "Running Bear" these days, some Native Americans may view that one as a bit derogatory. Maybe not.

Cherokee Nation as done by Paul Revere etc. -- This one would be an easy translation to one guitar and singer for you. Downstrokes are us, make it sassy and you could use all barre chords actually.

Cher's :"Half Breed" *might* qualify...(Male singer would have to change the 1st person to 3rd, of course, easily done

REDBONE - A Native American rock band that enjoyed chart successes, may have a tune or two you could use:

"Come and Get Your Love" - Redbone!

"Wounded Knee" -- We were ALL wounded at Wounded Knee...

I've always included "Little Wing" in such a show. You don't have to be Jimi or Stevie to pull this one off nicely, a folk guitarist can emulate Tuck and Patti's wonderful version with simplified playing - while Tuck 'n Patti made a medley of Castles Made of Sand plus Little Wing, I've just done the Little Wing part of the thing for something like you have to do:

Castles Made of Sand/Little Wing


--Mac