Plasma Cutter Power Cord too Small?

I think the clue is in the phrase "light duty", i.e. plenty of time off load, not being used most of the time. For 30 to 40 amps continuous this table seems to suggest 10 or 8 AWG for multicore up to 3 cores. But a light duty appliance is by definition not used continuously. The makers ought to mention maximum duty cycle somewhere in the manual.

http://www.engineeringtoolbox.com/wire-gauges-d_419.html

30% @32a

There you go... used 30% of the time. Spending the other 70% cooling down. Lincoln Electric say "Duty cycle is rated as a percentage of a ten-minute period. For example, a 60 percent duty cycle at 50 amps means you can cut with 50 amps output power continuously for six minutes out of a 10-minute period. The higher the duty cycle, the longer you can cut without taking a break."

Based on that, you can cut for 3 minutes continuously out of a 10 minute period. The cord will be rated with that in mind.

Based on that, I assume it should be safe then. Thank you.

Most electrical equipment has a rating which will be different depending on whether it used part of the time or all of the time. Limiting temperature rise to an acceptable level is one factor, and another is equipment lifespan. Sounds like your cutter and its cord are specced for light use, as you clearly realise.