There is risk involved in both desoldering and resoldering. When desoldering, If you don't remove all of the solder and try to force the switch out, you risk tearing the traces on the pcb (the wires) that complete the circuit. When resoldering, if you leave the iron on the joint too long you risk melting the pcb and damaging it.
The risks, however, are minimal. I had minimal desoldering experience and did a full filco ergo-clear swap in a few hours and had zero problems. Filco uses RoHS compliant solder which is tougher to desolder than lead-based solder, but is still manageable with cheap Radio Shack equipment. I use a 45-watt Weller iron when resoldering which is overkill for small PCB work, but I've managed to never even kill an LED when soldering, and they are much more sensitive to heat than Cherry Switches. So again, just be careful if you're using a hot iron not to leave it on the joint for too long when soldering to prevent melting damage to the PCB, which could result in damage to the traces.
One thing I would advise though, is after you resolder the switches on, check to make sure they are all flushly mounted to the plate. Sometimes the clips that hold them to the plate are a bit loose and the switches end up not sitting directly on the plate which will put stress on the solder joint and make the switch feel like it's pcb mounted. It's an easy fix, just heat the joints up and press on the problem switch so that it seats properly, and hold it in place until the solder solidifies.
Good luck!
EDIT: btw, that is the desoldering iron I used for mine, and it works quite well. Just be sure to leave it on the joint for a couple of seconds before sucking or you risk only sucking half the solder out, and it's quite difficult to melt the remaining solder. When this happened to me, I would re-fill the joint with fresh solder before trying again. Also, if I were you I would grab an extra tip or 2; the one that came with mine melted halfway through the job. The replacement tip seemed to be holding up fine when I finished, so the first tip was probably just a lemon which can be expected at this price point.