If you're worried about it, disassembly is likely not needed on that gun. The holes can be fixed with patching or dowel repairs glued in with epoxy mixed with sanding dust (use clear wood-compatible two-part epoxy and mix with very fine sanding dust). Try to use a similar wood for your dowel - looks like an oak stock to me.
IF the wood is varnished, remove it using a gel-type varnish remover - leave just long enough to remove the varnish - not the coloration of the wood underneath. The new finish you should apply is probably raw linseed oilas that is what was used in the 19th century.
Cheers.