I have a Donegan OptiVisor so I can see and use a Weller PTR7 tip in my old TCP. It's 700F and has a 1.6mm end for delicate's.
I work the legs free one at a time, being careful not to overheat the board and lift the traces. Then clean it all up with a little drywick after the switch is off. Tin the new switch legs and solder it in place.
We had one of those multileg desoldering tips one place I worked, it was more of a hassle than it was worth. I always just cut the legs off the IC's first with flush cutters then desoldered the pins one at a time.
You might be able to cut the legs off the old switch, depending on how fine your cutters are. That makes it much easier to clean up the pads.
At least they are surface mount and not through hole switches.