A diagram of the CONTROL CIRCUIT is needed.
Only switch the control power not the main power to the step down transformer or the IGBT or MOSFET in a Welder.
An IGBT /MOSFET doesnt like counter EMF when the ground is pulled off.
Separating the motor control solenoid from the arc firing circuit should be easy
with a diagram.
A foot pedal has a variable rheostat in it ,it doesnt shut current off all at once
it goes from 0-high then high -0, you could put a switch in it for just off and on
like a 15 amp light switch But have to know how much current follows thru the circuit,shouldnt be much at all,unless something else is pulling some amps,on the same control circuit.
I like your idea makes sense good luck with it.