I don't think I'd refinish it. If the adaptor goes on without drama, just do that. It would hide the worst of the muzzle modifications. The buttstock ought to be repaired or replaced if you intend on shooting it. I'd lean towards a relacement stock for range time. The old stock can be left "as is" in that case.

But if you do decide to restore it, have it done professionally. The muzzle can possibly be sleeved and then the whole thing could be refinished. Leave the touch-up bluing for small repairs to minor parts.