I agree to you that mouse click damaging mouse but theres no optimal mini game that would work for this game. Maybe keyboard keys click to escape? That would make game harder I guess
optimal is always subject to the thing you want to achieve.
a simple mechanic is timing. have a metronom or circle and when the indicator is good, tap/click - does not matter. i think seed of the dead implements something like that. it is also about zombies and struggling ;-) you fill up a bar by clicking and if you click at right time it goes up, wrong time it goes maybe even down. but i think there was additional mechanic, like measuring how fast you filled the bar to give you better result or something like that.
point is, you need not make quickness of input device and hand be the mechanic. But it also can be rewarding. I know that from fighting games, quickly tapping to escape a hold and so on. But that was more like 2 seconds of mushing the controler buttons. it is a form of stress release.