The welders may not discharge the capacitors directly into the weld, there may be a transformer.
Where I used to work we had a projection welder for putting the lids on DIL-14 oscillator. It could store up to 2500 Joules in a big capacitors and it discharged into the welding transformer, which was very near the welding jaws. The welding transformer had a single turn secondary, and was connected with about 500 mm2 of copper. The current peaked at around 100 kA.