Often times it's best to go for a complete refinish rather than touch up especially when you don't know for sure what the original finish is. I've not seen one in person but I'm thinking it's an oil finish, it's probably Birch so if it's dark at all it's probably a blend of stain and linseed or Tung oil. Very difficult to match.
Birch is sometimes difficult to get an even stained finish, it often times wants to be blotchy, darker in the cross grain like at the pistol grip and such.
I just recently found some stain from Brownells that says it's specifically for Birch and soft woods. It works really well but it is quite dark. It does completely cover even with one coat and not blotchy at all. But again very dark.
I'm not finished with the stock yet so the jury is still out, I want to see what it does when I put some oil over the stain.
Link some pictures if you can.
In Memory of Paul "Dietrich" Stines.
Dad: Say something nice to your cousin Shirley
Dietrich: For a fat girl you sure don't sweat much.
Cue sound of Head slap.
RIP Muggsy & TMan
"If you are a warrior legally authorized to carry a weapon and you step outside without that weapon, then you become a sheep, pretending that JOCKO will not come today."