[Dark Skies]

If you already have the appropriate tool (or can repair it as per SoCal's advice) I still think you ought to try using the movement of the car to turn that nut - it has to be worth giving a shot first before destroying the nut with more aggressive means.

I'm not sure that welding another nut over the top is a good idea - you may need to put so much heat into it that the wheel warps at that point. Certainly the paint on the wheel will be damaged.

If you find you can't wrestle it off perhaps you might be better off cutting the wheel stud flush with the nut using an angle grinder, centre-punching and drilling outwards with a succession of larger drill bits until the nut collapses. True, you will need to get a replacement stud but that might prove the easiest, quickest and cheapest route.