This is how I did it
The switch is from Supercheap, $11.00, momentary ON push button switch rated at 16amps.
Numbers are: PLU120389 and SCS1027
You could probably make the adapter bracket flat and use double sided tape wads to make up the difference?
The switch has 3mm travel and does not make contact till it bottoms out which provides a little leeway with the depth.
I made the stepped adapter plate as it captures the switch and reduces the chance of it loosening over time.