sanwa buttons are really made for metal control panels... not wood... and surely not just bent plexi.
you are either going to have to find a drill bit to make a hole that TIGHTLY fits the button, wedging it in there without using it's latches, or choose a different button.
the time to choose your parts and materials is BEFORE you start cutting.
alternatively, make a metal overlay that can attach to your finished wood panel and make it part of the design.