what to put on grips after I sand down a protruding edge on a stock mod 37 grip and make it match. They are a medium oak finish now.

Try some Tung Oil on the inside of the grip and see if it will match.

Well, it depends on how the gun will actually be used, what the original finish was and how often you will shoot it and what your goal is.

When my Chief's Special (EDC) had the original wooden grips on it I stripped off the old worn original finish (some sort of a glossy Lacquer) and I used 6 - 8 coats of Hopes 100% Tung Oil. It gives the grips a nice satin luster, wears very well, and once a year I'd just add two additional coats ( takes minutes ) for longevity of finish. The Tung Oil did not replicate the Factory finish but at the time I was interested in practicality not collector value. I've since changed them out and my current grips are not wood. I have since restored the Factory grips with a more glossy lacquer to look Factory once again, but they currently live in the original box.

To replicate the original Factory finish (if that's what your intent is) depends on the era they were made. Smith changed their wood, stains, finish and patterns over the years. The early years tended to use a darker stain and a more satin finish where as in the 80's the wood was a lighter color, slightly thicker and more glossy finish. You did not date the gun so I can not possibly give you any meaning full answer as to exactly what to use to replicate the Factory look.

Pictures would be helpful.

OldChief is giving you great advise test a small place on tne inside until you get it like you want it most of all be patient very patient and you results will be exceptional .Post us some before and after when you are thru .

Birchwood Casey Tru-Oil Gunstock Refinish fairly well replicates the color and finish of S&W stocks from the 1960's-1980's. Apply 3-4 thin layers with a clean cloth and use a brush for the checkering. Older S&W (pre-model number) stocks seem a bit darker and better matched with Minwax Tung Oil Finish with the same technique of applying 3-4 thin layers with a clean cloth and use a brush for the checkering.

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Scoundrel & Ne'er-Do-Well

This mod 37 is abj prefix, I think 1982, has a lighter glossy look. I have used tru oil in past, dont know if will work here.