I have repaired many triggers suffering from this condition by simply re-sharpening the trigger bevel (to the specified factory angle) according to the correct "bench-top" method taught at the S&W armorer's school. Usually, no further intervention is required.
Carefully check the SA cocking notch on the hammer with a magnifier to see if it is damaged. The notch is very shallow. If it has damage or has been altered you should be able to determine this very readily by examining it with magnification. If the hammer notch is damaged you will need to purchase a new hammer. The trigger can often be sharpened, as stated above. Sharpening involves the correct stone and following specific factory written instructions. Work on the components should always be confined to the bevel on the trigger. The cocking notch in the hammer should never be touched or altered.
Testing for push off requires what S&W calls "nominal pressure" be exerted on the back of the hammer spur after clearing and cocking the revolver in single action. This nominal pressure can (should) be exerted by using a trigger pull gauge attached to the back of the hammer and exerting approx. 10-12 pounds of pressure. Too much pressure can damage the components.
Sometimes, when previous owners have substituted an altered or lighter aftermarket rebound spring, a confirmed push off condition can be repaired by simply returning a full length, 17 coil OEM rebound spring to the gun. A light trigger pull (below 2.5 pounds) measurement can be an indication that the rebound spring may have been cut, or a lighter spring substituted.
Remember not to cycle the action under mainspring tension with the sideplate off, and be sure to use a quality trigger pull gauge after any work is done to verify the trigger pull is at or above the factory recommendation of 3 pounds.
Replacement "period correct" hammer/trigger combinations are sometimes compatible with the new frame, but minor fitting may be required.
"Stainless" triggers ( non-mim) are surface hardened.
If you are familiar with disassembly and would like to learn the simple technique for the repair of this "push off" condition, send me your e-mail. I can provide photos. It's very simple and effective, and you'll only need a 6"x1/2"x1/2" medium Norton India stone.
Carter