When I worked on replacing a switch, I started by using the spring-loaded desoldering sucker. Once I gently heated the solder I put the pump right down over the top of it and released it.
While that cleared a good deal of it, there was still some left holding it to the holes. What worked for me on the last bit was to gently pull up on the switch while applying a little heat first to one leg of the switch and then the other. That allowed me to start slowly backing the switch out and after a few tries of that the last of the solder let loose.
Once I got the switch out I used the desoldering sucker to clean up the last little bit of solder on the pads.
Like others have mentioned one of the big hazards is applying too much heat or for too long. You won’t need a lot of heat, just enough to start making the solder melt and don’t let the iron dwell on it too long.
It’s also key that the tip of your iron touches both the leg of the switch and the pad so that both are properly warmed to release the solder. I usually try to angle the tip so that it’s touching the leg more than the pad since I’m afraid of burning the pad.
Good luck! Hopefully some of that is helpful 