I wouldn't worry about it. Anything that's worth using, should be rated for comparable transients already (namely, EFT and ESD). As far as same vs. dedicated mains circuit, I'm not sure, there might be something there.
The proper place for a MOV is at the stinger and work. It is the instant of breaking the arc, where current drops to zero suddenly (and usually pingpongs back and forth several times, making a rapid burst of very brief sparks), that generates noise. The high voltages can be clamped by something like a MOV, and the ideal location for it is as close to the contact as possible.
Which is also why you should place a snubber across a relay contact, for example, not across the relay coil or solenoid or motor or whatever inductive load. You generally don't want to place MOVs across contacts, because MOVs gradually fail over time, breaking the isolation of the contact; but this would be the preferred place if not for that.
The next best thing you can do with a welder, is put the MOV at the output terminals, and accept whatever noise is generated by load current times lead inductance -- a few meters of cables, strewn about haphazardly, will probably amount to a few 10s of uH inductance. That isn't a lot, but we're also talking ~100A currents, and energy stored goes as the square of current. It's probably still enough to generate that rapid-fire burst of sparks, is what I'm getting at.
And this, finally, is why I'm skeptical that there's much problem with conducted mains noise -- the noise is generated by the spark, and merely carried through everything else. It's not generated by the welder, in and of itself, and indeed it's filtered to some extent by the transformer.
More to the point, you've got cables laid out randomly, without regard for signal quality or RF grounding -- it's an enormous antenna, and the EMP from breaking the circuit will pretty much go anywhere it pleases. Probably as much is conducted through the transformer, as coupled through common wiring, and grounding, in the welder's encloure.
These are fast events -- a spark can break down in a fraction of a nanosecond. In a nanosecond, the wave thus emitted, travels a mere third of a meter! It's an instant to us, but it very much expands like a shockwave, pushing things out of its way as it expands -- fortunately the radiation pressure is minuscule, it's hardly a physical push; it's more an analogy for the voltages/currents in conductors that the wave interacts with. (If we're talking peak voltages of 4kV or so -- a typical high-level EFT waveform -- then we're talking peak currents around 10A in free space itself (having an impedance of 377 ohm), or higher in transmission lines that have lower impedances, roughly 100 ohm for mains wiring for example.)
Tim
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