Good way to switch AC/DC (Rectifier) in welder
I'd guess your best bet is a starter contactor for an automobile. You can get 100 amp units for less than 20 bucks, and you might do a lot better at a junkyard. They typically aren't rated for continuous duty, but I'll bet your welder isn't either.

You can get away with this because you aren't attempting to activate or deactivate the switch while current is flowing, and there isn't much voltage across your bridge.

You'd need to make a little 12 volt supply for the coil, but that shouldn't be too hard.