"I assume it is really the voltage under load that matters and not sure how to check that."
Best way is to already have that multi-outlet setup you're talking about (and I already have) - then you can have a helper run (watch) the volt meter (as close to the machine as possible,
NOT at the dryer outlet 
- you can check non-loaded voltage first, then have the helper watch the meter while you do a cut. Hint - first make sure the
meter is NOT on "auto-range", usually they have a Range button you push ONCE to lock that range with a stable input, then successive pushes increment/decrement the range.
Without a multi-outlet box, you MIGHT be able to pull the PM45's plug out just far enough to get the meter leads to touch both hot pins, but this is
not for the faint-of-heart or shaky-of-hand, or a wife that's not used to being a helper -
If I were you (as in, haven't built that multi-outlet box yet) I would do that first - I'd use heavy enough wire (#6 on mine), and use a nema 6-50 plug and sockets - then you could just plug THAT into your extension cord, plasma into one of the females and test leads into another (you'd still need a "watcher", and still defeat auto-range) -
You may wanna make your multi-plug just long enough to reach your intended NEW weld plug from wherever your welders will be, and make another extension for use when you need extra reach - I have a 6-50 extension that's 85 feet long with 2 females, another that's 25 feet with 3 females, and one more that's 10 feet with 3 females (did I mention I like OPTIONS??!?

)
I mount 1 6-50 female per 4-plex deep box, and for multiples I'll knock out TWO plugs between 2 boxes and tie them together with 2 chase nipples - this keeps them from wanting to rotate on a single chase nipple - Also, with that heavy a wires it lets you run the "daisy-chain" thru BOTH nipples, typically 2 hots thru one nipple and ground/neutral thru the other.
For running over rough surfaces, and for circle cuts - I use one of these
Plasma Cutting Guide | Flange Wizard
check out the whole page, they also have a bevel guide that works with it. 2 wheels with straight cuts, set just enough tip height to clear the "crusties" - for circles a single wheel works well, check the page for more... Steve