Put masking tape around it to start with to help protect the wood (already mentioned above). Maybe use some Scotch tape (as it's thinner) when it's almost flat. Then sandpaper should work after the files. Make sure the frets stay covered as you don't want to scratch those. Don't use too coarse a file or paper, as MOP is supposed to come away in grains that are about twice the size of the grit used, so you can easily get dips below the surface of the fretboard. So go fine and go slowly but surely.