I've seen several quotes regarding people carrying tomahawks in their belts. We've now seen a couple of examples of shoulder slung sheaths, so we know they existed.
This quote is from George Frederick Ruxton's lesser known book,
Adventures in Mexico and the Rocky Mountains:
Note that he took the trouble to mention the "...large butcher-knife
in a sheath of buffalo-hide..." and "...
a little buckskin case containing a whetstone..." He didn't say anything about a tomahawk sheath, though. This is not to say the tomahawk was
not sheathed, but he did mention sheaths for the other two items.
For certain, I haven't read everything. I have read a lot, though, and I have seen mention of people carrying tomahawks in their belts a couple of times, but I don't recall reading any
specific mention of a tomahawk sheath. If it were me, I would probably try to fabricate one using traditional materials and techniques. If nothing else, you could just fold a scrap of buckskin over the cutting edge and wrap a thong to secure it. If our hypothetical trapper had to "whip it out" in a hurry, he probably wouldn't take the time to uncover the blade.
As a parting thought, it is my understanding that most of the surviving native tomahawks of the types that would have been used in battle have blunt, rounded edges. These were used more like clubs than weapons for cutting. However, it would make sense that their camp axes would be sharpened, and I believe Samuel Hearne stated that they used files for this purpose. It would also make sense that the white trappers would sharpen their axes, as the axes would be used for cutting stakes and so forth in setting beaver traps.
Just to add a little to the confusion ...
Notchy Bob