Solder flux will not cause a short circuit. It is critical to a good joint. Flux stops oxidation of the metal when heated to temps high enough to melt the solder. The joint should be cleaned once it is set, which eliminates any stray acid from the area.
The original brushes were soldered on, why couldnt the new brushes be soldered also? Welding also introduces voltage to the starter, which could harm something inside it. Care has to be taken not to overheat the brush pads, and everything would be ok. .
you`ll never get a grinder into that small area. A dremel, maybe, but you risk damaging the solder pad, which could easily be de-soldered with the correct iron.
-j