I've got a 1950's Marlin 336 that was my grandfather's. Before coming to me, another relative had the left side of the receiver drilled and tapped for a 4 screw hinge-style scope mount.

My question: is it possible for a skilled gunsmith to weld or otherwise fill the screw holes to make the receiver look original and undrilled? I do not want to use filler screws if I don't have to. I know it'd probably be cheaper to find the same unmolested gun but this was my grandfather's so I'd like to spend the money on this one if I can get it done for a fairly reasonable amount.

I know that if it is possible, I'd need my gun reblued and I'd like to have that done anyway. I do not care about any collector value as it'd be one of the last two guns to leave my possession.