The grips look like the finish is already stripped off, mostly. I say stripped because the wood and checkering look great, not much wear. I don't know for sure what S&W used for stock finish in the '30s but sprayed on laquer was pretty common then, for example Winchester rifles. You could try some rattle can lacquer applied in very thin multiple coats. If you don't like it a soak in some lacquer thinner will return you to where you are now, no harm done.

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Hand tighten only