I wouldn't be surprised if the User Manual for the welder talks about extension cords. Many appliance/tool manuals do.
The entire problem is voltage drop caused by wire resistance. About the biggest extension cord you can get is #12 AWG and it will probably work fine for your 15A welder out to 100 ft. Probably... Not guaranteed... When you start stacking two extension cords, things might get a little iffy at 200 ft. But it's the welder that will have the problem with low voltage, not the cords and certainly not the circuit breaker or fuse.
Or, maybe the idea that the resistance is so high that a short circuit won't trip the breaker. The breaker should trip at 10x nominal so a 20A breaker should trip at 200A instantaneously. Every other kind of trip is 'long time' and has to do with long time overcurrent. Possible, but not likely. So, the question is, could you have enough resistance to preclude creating a 200A short circuit. 120V / 200A = 0.6 Ohms down and back and, as luck would have it, the resistance is 0.685 Ohms for #12 AWG. There is a slight possibility that a short circuit won't trip the breaker. But it will trip pretty soon on 'long time'.
I would just try it and see how things work out. The duty cycle for these small welders is pretty low and the cord has plenty of ventilation.
If you want to do this professionally then there are some heavy duty extension cords in the marine industry but they are pricey:
https://www.westmarine.com/electrical-cord-setsYou can also buy the cable and add your own cap and body. The problem is, most 20A devices won't accept really large diameter cable. You will probably want to buy a couple of adapters and use the standard marine connectors (or something very similar).
https://www.westmarine.com/adapters-plugs-outletsMotors on extension cords will have a hard time starting because they draw around 6x full load to start. Maybe more... The voltage drop will also cause the motor to overheat. Not using an extension cord with an air compressor is probably good practice. That said, I have done it with my little DeWalt pancake compressor. I won't do it with my bigger compressor.