Before serious grinding, first run the whole perimeter of the piece very lightly against the grinder. This removes the worst of the 'scalpel' edges and avoids the micro cuts on your fingers.
Let the grinder do the work. Many people seem to put huge pressure on the piece to grind away the waste more quickly, but this is actually counter-productive. Less pressure means less fatigue, less chipping at the edges, fewer broken pieces, and most importantly, fewer cuts to the finger tips.