Plus 1 for the flap disc. i have a battery powered 125mm angle grinder, couple it with 80grit discs and a gentle touch, they are very effective on the belly cut.
Just wear gloves, a respirator, goggles and make sure you know where all of your fingers are in relation to the disc at all times. There is a nice little scar on my fret hand middle finger as a continuing reminder for me.