...but a shunt that was part of the inherent current carrier as Greg suggested is a low impeance source and would be verry consistant in manufacture and use.

Yes. But don't forget, that the circuitry (cables!) sits very near to welding spot, and enormous interference in the differential amplifier will be caused by induction. Only a design with minimized loop areas (twisted pair cables) and extensive magnetic shielding will satisfy, if at all.

Kai