I am going to disagree.
1 3/4 inch long that were hand screwed (no drilling) into the wall.
Assuming that the material you made the French cleat out of is 3/4" thick and your drywall material is 1/2" thick, that means that your screws only penatrated the drywall by 1/2".
Assuming that your wall is a standard 2x4 wall, any wiring would be in the center and 1 1/2" away from the drywall material. Any closer than that and a metal plate should have been installed to prevent you from hitting the wiring with a nail or screw.
Even if you hit a wire with a screw, that would not cause the switch to to make a popping noise. Either the noise you hear is normal or the switch is defective.
Any popping sound caused by arcing caused by hitting the wire would be at the screw not at the switch.
Chances are that this is just something you simply didn't notice before. Only notice it now because you are worried. If it makes you feel better replace the switch.