I have this same hawk.
I like it, but I would really like a good camp knife too.
Kleanstrip Premium Stripper melted that paint right off for me.
It worked very well and was followed up by scotchbrite pads to remove any left overs in the texure of the metal.
I removed that set screw and sanded the handle until the head wedges towards the upper handle by swinging it firmly.
I have not put a finish on the hawk head yet, but I am toying the idea of a food acid patina, later halting the patina process with baking soda and then covering with an oil coating to prevent any rusting problems.
I did this with an Opinel knife using mustard and it looks pretty good after sharpening. I have had no rust issues with this knife at all.
Still plum browning would look better, but you would have to eliminate the texture and that would change the temper hardness on this hawk head.
The metal texture might also be an issue with the patina method mentioned above, but I am still thinking of trying this.
I already wood burned a salmon graphic on both sides of the handle where it is grasped, and will put small turkey and quail tracks, hog tracks, bear tracks, mountain lion tracks, in wood burned graphics along the the handle and carve a mule hoof on the bottom handle end.
I have yet to make a sheath for it, because I have not settled on a design. I would want to access it quickly out of a one piece snap top covered belt sheath.
This hawk is great if you want to modify it, but it is a tomahawk from our time in the current day.
Still, I am sure someone from the past would have loved to have one of these.