Assuming that the holes are large enough to accommodate it, a Dremel or trim router with a flush cut, bearing guided straight bit provides the neatest, most accurate cut. Otherwise, a very sharp knife such as an exacto knife will work.
The bit (credit to Lee Valley for the image
The trim router I used (set up for inlay - not cut-outs) :
The cut-outs using a trim router and flush cut bit as pictured above :