I agree with whats been said. Just want to add... a router will not make 90 degree corners. You will need to do the final cuts with a chisel.
Even with a router and template... you could get a crooked result... if you have not measured and aligned the template square.
Btw.. from your pictures... it appears your buttons are quite far apart. (it might be an illiusion because there is no buttons in there yet. I suggest spacing buttons so that there is just enough room to turn the button nuts.
Another option not mentioned.. ( I think.. as Ive been away from the post for a while.. in mid post ) Is that you could cut a larger square, and glue in a wood hole plug, or inset a wood frame, or place a metal plate over the area (much like a trackball mounting plate).
If the area is to be artworked over... some epoxy putty can fill any gaps, then simply apply the artwork, use an exacto and poke through it, carefully trimming the art to the edges. (probably best to clamp a straight edge right up to the cutline to keep the material from possible stretching / tearing... as well as to better keep your blade straighter in the cuts) Even then, if the cuts are a little less than perfect, you could use a pinstripe outline.. or glue pieces down over the top. As well as possibly using spray paint / airbrush, with a template (or removable tape).