I would suggest that if you can wire the circuit in 10 gauge, do that. But use a 15A outlet and the 20A breaker. Make sure you're either using an HACR breaker, or something made since 2009 (after which the HACR standard was absorbed into all breakers).
I very much doubt you'll experience breaker trips, on a 20A breaker. The instantaneous trip curve for 20A breakers is not significantly different than the curve for 30A, and the thermal portion of the curve (where there is a big difference between the two) isn't going to come into play with a spot welder (certainly not at 50% duty cycle).
The blades in 15A, 20A and 30A plugs all have the same amount of metal in them, so they can all carry the same currents. They're different configurations, solely to prevent dangerous interchanges.
The 10 AWG wire will have less voltage drop at the ludicrous inrush current that a spot welder uses, compared to the 12 gauge, so it may weld better with it. But at the 50% duty cycle, 14 gauge would still not overheat, so there's no safety concern about using 12.