Can't use plexi? If you're just thinking about the thickness being too much, why couldn't he use thin plexi, like 1/8" or even 1/16", or rout the underside of the wood a bit?
Or are you thinking he's backlighting, and the light would shine out through the plexi? I was considering doing this, and was concerned about the same thing. Best solution I have thought of is to paint the inner edge of the button holes black, plus a thin strip of black on the top, around the circumference of the hole, to shield under the lip of the button assembly.
Or is there some other issue I haven't thought of?