I agree with Greg, but...the 'gray area' is how often is the welder moved? "frequent interchange" (400.7(6)) is open to opinions. If you are the compliance officer, that would be your call. Common trade practices on my side of the Hudson is Chapter 3 wiring to a receptacle, and a cord with cord cap on the unit.
The second part of your question (pigtail) IMHO is NO
Sounds like the cord is being used for fixed wiring. Again, the term 'pendant' is not defined within Article 100, and is also a 'gray area' and subject to opinion.
Article 400.7 & 400.8 spell out the 'can & cannots' for rubber cords.
