Will it be exposed or will it be covered by a pickguard?

If exposed, you'll need to keep it very neat (even with a pickup surround). Whilst Forstner bits are a good way of removing a lot of wood, unless you have good chiselling skills for the final removal, you may find that finishing off the sides with a sanding drum on a Dremel is easiest. My woodworking skills are such that I certainly wouldn't do a rout for a body-mounted pickup (with no surround) without using a router.

Don't forget that the central spike on a Forstnet bit (depending on its diameter) can be between 3-5mm long, so allow for that when drilling and don't go deeper than you need to as you don't want holes poking out the back.