I've seen buzz boxes go up in smoke when welders tried to extend their duty cycle while welding at high amperage. Poof, a few flames, a lot of smoke, and then nothing!
A more realistic determination of the power used by the welder in a shorted condition is to measure the input voltage and input amperage. A single phase machine for home use, i.e., 225 amp buzz box, will require 220 volt at 60 amps to produce the maximum output. In a dead short condition, the machine can produce more than 225 amps, and it will toast the power supply if the duty cycle isn't adjusted for the actual current draw.
If you reduced the current to the point that the duty cycle is 100%, the current will not be high enough to produce an strong magnetic field by passing AC through the weldment as you suggest. The strength of the magnetic field produced is proportional to the current passing through the part. To buck the magnetic field produced by the welder using DC, the AC would have to be as high as the DC. However, only one half of the AC would buck the DC, the other half of the AC cycle would be additive to the DC thereby doubling the strength of the magnetic field on that half cycle.
However, I'm not totally adverse to your idea of using AC to counter the magnetic field produced by the DC. I would be willing to use the AC to energize several turns of welding lead wrapped around the part being welded. The theory is that two separate magnetic fields can't coexist in a part. The magnetic field produced by the AC would be longitudinal and would switch polarity 60 times per second. It would disrupt the circular field produced by the welder using DC. The beauty is that because the strength of the magnetic field is the product of the number of turns times the amperage, the amperage draw on the AC power supply could be relatively low and within the adjusted duty cycle of the power supply so as to prevent overheating.
I've never tried running AC through the wrapped welding leads while welding with DC, but it does sound feasible provided the field strength is not overwhelming and disrupts the DC welding operation. I do know that the solution I originally proposed works because I've done it many times and I've even performed the degaussing operations during welding operations if the residual magnetic fields became severe enough to upset welding operations. Energizing the wrapped leads with AC while welding with DC is an interesting concept.
Now, the trick is to actually try it.
Best regards - Al