The right bit is called a slot cutter. Home depot has them, you want the 1/16 inch size. You also need to get the arbor, which is the shaft the bit mounts on. The manufacturer is Oldham. The job will take just a few minutes with this bit instead of a dremel, and will be perfectly straight. Wear some gloves, though, your skin will get sand-blasted with wood, no joke! It looks like this:
