Flexible cables for cords use table 400.5(B). #6-2 90°C Type W is rated for 99 Amps.
Personally, if it's cord-and-plug, I'd size OCPD for the cable & plug, too, regardless of what 630 says, because *anything* could be plugged into that receptacle. The breaker is designed to mimic cable heating, so (in theory) it shouldn't trip prematurely if the welder's duty cycle is OK for a 50A plug, even if current exceeds 50A.
