Many appliances (eg: portable AC units) say not to use an extension cord because most people have dinky little lamp-grade extension cords that would pose a significant fire risk. So the appliance manuals say never to use an extension cord, when you just need to get a sufficiently heavy-duty cord. Welding rigs can run on suitably heavy cords (10 gauge), and they can pull humongous loads.
Personally, I’d get a 12 or 14 gauge cord, because then I could also use it for a portable AC unit if I ever wanted to. 25ft 14 gauge cord can handle something like (back of envelope here, don’t quote me) 1800+ watts, 15 amps at 125V. In fact, I might just go buy one just in case now that you’ve reminded me.