Hello,
The thing you want is called "tact membrane switch".
The button press is "clicky" because of the metal dome on the switch : nintendo switch, 3DS, xbox one, gba sp are using this.
Thoses buttons are indeed cool to use, but i think the rubber "thing" between the button and the switch has to be adapted for that kind of use.
On gba sp the rubber is super thin when there is no rubber at all on xbox one (and the dpad on xbox one, for me, feels really good). a spacer between the dpad and the membrane switch has to be made, 3D modeling and a lot of testing is needed.
It is possible, but the guy behind this mod needs time and skill to complete this