I might get beat up a bit by the more label-conscience sticklers (who are, actually, right...) but I think you'll be fine with that. There are lots of variables here, as the actual current draw will depend upon your welder settings. The two issues here are the voltage drop at the welder end of the cord...meaning you start with 120V at the receptacle but will have some lower voltage at the welder under load. Will the welder work okay? In my experience, yes. That cord is at the smaller end of the range for a 15A cord 100 feet long. The other issue is heat within the extension cord, under load. Out in the open air, on the ground, I don't see an issue. Just don't coil the cord up inside an enclosed container filled with old oily rags..which you're not going to do.
I've run bigger welders on much smaller, and lots longer, wire runs in other countries and had no issues with welder performance or melted wire.