I fully understand what you mean and want. I think the only option (or using complex servo controllers etc.) is such a small solenoid.
See here example:
Off course I do not recommend a heavy solenoid, but one fit for purpose. And yes the top of the head you must protect from not pressing the metal to you switch. But this is just a “mechanical” thing. Glue (2comp) a rubber piece like this:
If you do wish to swap out the switch, then note that the master switch isolates both the phase and neutral, so a 2 pole switch. I would recommend getting proper industrial equipment, this is mains and heaven knows what sort of current is flowing through those wires.
There are some threads around here on more industrial style kit. This is not a job for some cheap chinese relays designed for light bulbs or other low-ish current circuits.