I am not sure LOL, depends what you are calling Gnd wire. The Screen is what you want to connect to the Gnd terminal you have circled in Yellow.
Yes you can remove the switch as long as you keep the circuit intact, that will depend on how they are presently wired. Normal practice is to have your switches wired in series and use the Normally Closed contacts on the switch, so in the pic above you would feed the wire from you BOB to the C on the first switch then from NC on first to the C on the next switch, then NC to C on next switch etc then back to your input on the BOB. You can do this with all switches and just use one input or you can if you wish have separate circuits for each axis and use 3 inputs.
If that is the way you have them wired you can remove the faulty switch and just join its wires together to keep the circuit intact.
Hood