If you want to use period correct materials one option is cutler's resin. I make mine of pine pitch, charcoal and beeswax. You can change the filler. Charcoal in this case will give you black. Ashes will give you gray. Horn scrapings/sandings will fill worm holes in horn, etc. Do this outdoors and don't catch yourself on fire as the stuff is like napalm, sticks to you and burns deep.
I find pine pitch, get about a 12 oz can filled with it and heat it up till it's runny over or to the side of a fire. I strain it though another pre-heated 12 oz can with holes punched in the bottom into a smaller soup can. Take some charcoal from a log that's half burned and pound it with a mallet till it's powder, then strain it through a wire mesh. Add about 1/3 volume compared to the pitch. Now add about 1/6 volume beeswax. More beeswax if you want it flexible (not needed here). Mix it all together over heat. When it is uniformly mixed, take some sticks like popsicle sticks and dip them in like you were dipping candles. Dip. let it harden, dip again, etc. Leave a handle of 6" w/o any resin on it. Now you can heat this over a stove or fire, get some molten stuff ready to run off, and patch your holes in most anything. A couple of these sticks should be in your kit when you go a trekking for a few days. It was called cutler's resin because knifemakers would use it to fill the holes in "through-tang" knife handles. It has been around since cave-man days. I've used it to patch defects in tool handles, fix cracks, stabilize loose axe heads, etc. It will clean up with turpentine. I have successfully varnished over it.
OK, another option is a wood patch and we see many of these on original European guns.