Take it to an auto body shop and ask them to weld some slag or drip some lead on it. They probably won't even charge you anything because it would be the weirdest thing they did that day. And they would be able to grind that line pretty straight.
I could be wrong, but I would imagine the heat from welding would do some damage to the base (I'm no expert, but I do stick metal things together occasionally with my MIG setup). Maybe someone really skilled with a TIG setup could do it without excessive heat...
I also don't think too many shops use lead anymore, plus I suspect the lead would wear quickly since it's much softer.
I haven't seen enough repairs to really judge, but I would see how it feels riding. If it's terrible, take it back to the shop and ask them to replace the damaged section of edge. If that's too expensive, then what Weipim said.