Measuring the voltage outside the welder creates some interesting problems, because TIG welders have high voltage radio frequency ac (pilot arc) superimposed on the main high current dc.
To measure that requires high bandwidth, but the wideband noise from the arc is going to make nonsense out of anything you can monitor.
Kind of like asking how can I record a close intimate whispered conversation in the presence of a heavy metal rock band going full blast. Its not really possible.
Back inside the guts of the welder, the dc current can easily be monitored before the pilot arc rf is added, so its not a problem there.