easy job or buy a new trigger
The S&W triggers are casehardened, so a file is not easy to use. A Dremel tool is not really easy to use.
I like a round diamond sharpening tool used for knives and fishhooks. You really don't need to do more than remove the sharp tops of te grooves.
Use a properly fitted screwdriver. Often you have to fit a screwdriver to the slot for a correct fit.
Do not try to pry the sideplate off, rather use a plastic, leather or wooden mallet to tap the grip frame down, inertia will loosen the sideplate. Keep track of where each screw was used, they are different.
Carefully [use eye protection] lift the rebound slide to release the trigger.
Lift out the trigger by using a toothpick or other soft tool to move the hand out of the slot and lift the trigger off the pin shaft. Note how the hand spring is installed.
A vise makes it easier, but you have two hands for a reason. If you do use a Dremel, a vise is a must have.
Clean all metal particles off and out, use canned air after a solvent wash.
Reassemble.