I made a leather blade "sheath" for mine--I have three. Thrust through my belt on right side rear, just over the hip. It rides well there, and is readily accessible. I take it out of the belt if I want to sit in a chair, but it's not really a problem if sitting on a rock, log, ground, (maybe even a horse).
Newman's book, Swords and Blades of the American Revolution, illustrates tomahawks being carried in a similar fashion. The pictures show the blades being wrapped in cloth or perhaps buckskin. PC? Maybe, maybe not. Meh. It works.
I read somewhere that tomahawks were carried more often than a pistol, and IMHO, a tomahawk will certainly cut or chop better than a pistol will. We do know that the members of the Lewis and Clark Expedition each carried a tomahawk as part of their issue equipment. -- JB