Ive done this a few times, and even for really big difference in pickup size, just for the small amount of wood you would need to remove, I would use a drill press and a forstner bit.
Here's my way of doing it, YMMV
1)Make a template out of paper and transfer it to some clear Plexglass from your hardware store. be very careful when cutting the template (use eye protection, should go without saying...), use a drill to start a pilot hole and a handsaw or a power skill-saw with as many teeth as you can find for the real cut, cut it just a hair (like 1 mm) inside the lines you transferred from the paper template and sand it to the line straight with a file or sandpaper.
2) Secure the template to the bass with double sided sticky tape, make sure you get it exactly straight, (use an enginers square or a quick square).
And secure the bass body on the drill press (I use a few rubber bungee straps) make sure it doesn't slip or slide.
3) Align the largest forstner bit, with the drill OFF, to the place you are going to make the first cut.
4) Power on the drill and drill it flush with the existing pickup cavity. Align the bass for the next cut and repeat, just be sure you don't let the bass or the template slide before or during the cut. Take your time and do a clean job.
5) clean up the forstner bit "holes" with a wide wood chisel (gently) or a sanding block cut to fit the new cavity, sand slightly to remove the tool marks.
6) Make sure you have enough clearance for the wiring to make it through the hole for the previous pickup, and still have enough slack to do the soldering thing...
If you lived close I would show you first hand how easy it is!!
Good luck and enjoy !