Hello Mario:
You asked for opinions and I will give you mine: the firearm (I do not understand if it is a shotgun or a rifle) is of not high value (I mean market value, not sentimental value) so just make some refinish for the wood (a little sanding and some kind of oil finish) and that is. If you can make the small piece of missed wood, fine, but it is not escential.
Perhaps you can make the refinish by yourself saving a lot of money. I once made a wood refinish for a shotgun with a Brichwood kit, without previous experience, and the results was really fine. Little sanding, little filler and lots of oil finish rubbing.
Good luck with your proyect.
Best,
