Yes, but the outer casing slides in front of the panel so that's not the limiting factor on the back of the panel.
You could even cut a slot in the panel and mount a leaf microswitch there. You could have it practically flush.
So the button itself is captive in the outer casing? There still has to be some clearance between the inner and the outer.
It is very difficult to access the back of the panel, because it is like an unified entity, four walls so to speak, with a little space from above and only accessible via the bottom, which is secured with a security screw, for which I don't find the right spanner tool for the moment (and probably I'm forbidden to do).
Maybe one can drill through the plastic, but behind it there is the battery holder, so not really advisable to do if you don't want to damage it.
You can probably completely dissamble the meter, but I think there is a high chance that you will tear it completely apart due to the brittle little micro screw in it and so on.
But I appreciate your effort to solve my problem.