There are only two basic types of front sights on S&W revolvers, pinned and forged integral with the barrel. If your sight is perceptably loose it is a pinned sight, whether you can see the pin or not.

Go to your local auto parts store and buy a can of brake cleaner, one which is Perchlorethane or Trichlorethane, not one of the non-clorinated types. Also buy a tube of one of the "wicking" types of Loc-Tite, the stronger the better. Spray the sight thoroughly to flush all oil from the rib and sight tenon, blow out with compressed air. Repeat at least 3 times to be sure the area is clean. Once cleaned apply the wicking Loc-Tite and let it cure thoroughly, several hours. Once cured clean the excess off the rib and sight with the brake cleaner on a rag and then oil. The loose sight problem will be cured permanently. Only the part of the resin that penetrates into the sight slot will cure since Loc-Tite products are anaerobic resins, they cure only when air is excluded. That which is exposed on the surface will thicken a bit but can be easily cleaned off. This way you don't have to remove the pin.

This is an extremely common problem with guns made in the 1950s and before with target sights.

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Gunsmithing since 1961