on the side it has:
16(6) 250 <sine-curve symbol>
10(4) 250 <sine-curve symbol> <pole-with-wire-wrapped-around-it symbol>
It has 3 spades and two screw terminals.
Does this mean it has two "modes" ie 10amp and 16amp?
Ie it is not a simple on-off but a: 10amp-on and 16amp-on and off switch?
Or maybe when the switch is on, it supplies both 10amp and 16amp?
Is it an illuminated switch? Does it illuminate when it's switched on or when there's a fault condition?
Can you trace the wires that went to the switch - I suspect the screw terminals go to the mains input, the other pair to the contactor and the odd one to the thermal cutout. If the latter is correct, you will need to get the live & neutral the right way round - refer to the notes you took before removing the switch.
The 16(6) Rating is is 16 amps resistive load, 6 amps inductive 250volts AC (sine wave)
I'm guessing the 10(4) rating is 10 amps is 10 amps resistive, 4 amps inductive 250 volts half wave or DC, not sure about the wire round the pole symbol.
Do you have the instructions for the welder? Does it say anything about resetting the welder if it cuts out?