Would refinishing affect their collector value ...
Short answer, yes. Always. Even a refinish from the original manufacturer will affect what a collector is willing to pay. Collectors pay top money for one thing, a certain make, model, and caliber gun, in the best
original condition they can get.
Anything that changes that lowers what collectors will pay. Changes in the finish, mis matched parts #s, or maker codes, all theses things mean that the gun is no longer fully original. Doesn't mean anything to the use or function of the gun, just that its not what the collectors want most.
Example; WWII Walther P.38 in a local shop (GI bringback, widow consignment), complete with matching year holster. They were asking $900. Only trouble was at sometime, the owner had the gun nickel plated. Very well done, but it made it poison for a collector. No different than a 1970s Walther police surplus P.1 for value. IN other words, gun only has its value as a shooter, because of the refinish. The holster is worth more, to a collector. I've got a 36 Luger, gun looks new. Was told it was refinished by the maker, during the war (but you get told lots of stuff....). one mismatched # part. Gun is worth (and I paid) about 1/3 the value of a gun in the same condition with original finish and all matching part #s.
So, take that old Colt, and do what you think best, its your gun, and while not common anymore, they aren't super rare. Just don't expect a collector to think its worth top dollar if you have it refinished or repaired in any way.
Best to make sure its not some uber rare variation before you have anything done to it. A really rare variation of a collectable gun in poor condition, but all original, including wear and flaws from use, might be worth more than a more common model in good shape. Collectors are funny folk about things like that.