Generally since the plate doesn't support switch removal you would have to desolder all the switches but it can be done without doing so. I have done it before myself, you will need to desolder the switch and led that is in the switch itself.
Here is a pic from a bare pcb without a switch but the circled pieces is what you will need to desolder.
After you're able to successfully desolder them, try to squeeze a small flathead on the other side between the plate and the switch and pop it out. Sometimes a nice may be better to loosen it as first. Make sure there is no trace of solder left or you could damage the pcb.
Is your soldering iron have temp control by chance? If not 60 watt is a little high but it's doable if you are quick.
I hope this helps, let me know if you have any further questions.