1) The double action pull on a pre-MIMS M17 should be no heavier than that of a similar vintage centerfire S&W DA. If it is, there is something wrong.
2) While I concur with suggestions about thorough cleaning, the first thing to do is to determine whether the unwanted drag is in the lockwork or external.
a) Put some fired cases in the charge holes, close the revolver, and gauge the DA pull for a baseline. Better if this is done with a trigger pull gauge.
b) Now open the cylinder, push the thumb latch aft, and cycle the trigger again, also gauging the pull.
3) If the open cylinder and closed cylinder pulls are about the same (both too high), the problem is in the lockwork. Unless you really know what you're doing, this is a job for a qualified gunsmith. Revolver needs to be completely disassembled, cleaned, and lubed. Check for drag on hammer boss, trigger boss, hand in window, and rebound slide. Be sure firing pin block is not bent. Check for flatness of the side plate.
4) If the open cylinder pull is less than closed cylinder pull, and normal, problem is exterior. Thoroughly clean cylinder window and front face of cylinder. Disassemble ejector rod, clean, and ckent for non-straight in internal rod. Remove extractor star and thoroughly clean under side and cilinder recess. If cylinder and star are rebated (almost always the case with rimfires) remove any crud from the recess. Check yoke for straight. Lube and reassemble, and then check barrel gap and end shake.
One other point: because .22 rimfire ammo uses externally lubed slugs, rounds do not drop freely into charge holes. If one or more rounds hangs up on seating, it will drag on the recoil shield. Solution is to thumb all rounds flush with the rear face of the cylinder.
As a general rule, I do not recommend lightened mainsprings for S&W revolvers. A very moderate adjustment of the rebound slide spring is less trouble prone, but even this should not be necessary to achieve a proper DA trigger break
