A few years ago I bought a write off SLK [panel and bonnet damage] also with the same problem and
the Laser ones did the job although I had to turn one down in a lathe as it was a few thou too big on the outside.
Looks like the later ones are already done.
They worked because there was a decent amount of the lugbolt protruding to wind on for a tight fit.
From your picture there doesn't seem to be enough of the nut protruding to get a good grip with this type of tool.
If this is the case I would chisel off the wavy bits left and weld a nut on.
Any competent welder can do this, the only risk, if carelessly done, is welding the nut to the wheel stud.