Have you considered doing it by hand? A couple of years ago I watched Garret Hack demonstrating stringing work at the Westonbirt Festival of the Tree and it really is quick and efficient. He uses a slightly tapering cutter to make a tapered groove which is matched by the stringing so it all ends up tight.
I was about to ask exactly the same thing. Spiral downcut bits seem to be recommended for the cleanest cut but the smallest diameter you can get with a 1/4 inch collet seems to be 3.2mm. You can buy a collet sleeve to convert a 1/4 inch to 1/8 inch though, which means you'd be able to use spiral downcut bits designed for use with a dremmel. Does anyone have an opinion on whether a spiral downcut gives a cleaner entry cut than a standard straight bit?