I've seen a few sheaths, most likely all early 19th century. With shoulder straps, and one that was mounted on a belt. However, I'd be willing to bet, that in the 18th century, a lot of people did just carry the tomahawk thrust under the belt, with no sheath over the cutting edge at all. I'm certainly not going to do that. It would be pretty dang dumb.
It is possible that these tomahawks were not particularly sharp. Seeing as how it was basically a weapon, not so much a tool, the edge doesn't necessarily need to be very sharp to drive it into someone's skull.
Mine has a sheath.
View attachment 122974