My guess is the weldingwire will break when the caulk is that hard. when I purchase a kit with the new sealer, and windowprimer, there also came a cuttingcord with it. It was a kind of rough stainless cable that eats away the caulk. I`d go to your local glass shop and ask for one of these. must be a $2 tool...
not sure if you need to paint the car, but since e-bodys have a pretty deep rabbet, its kinda hard not to scrape along the paint with a cord and not putting any tension on the glass at the same time.