Cutting a drywall hole for an electrical box with a router.
Most professional drywallers cut electrical box openings with a router. You'll be pleasantly surprised how quickly you can develop a feel for the process.
Practice with the new tool before you commit to a full sheet of drywall. Temporarily screw a piece of scrap drywall over an electrical box, then cut the opening. Shift the drywall to a new position, and keep trying until you become confident of your new skills.
To control the dust, purchase a dust hood accessory for your router. Hook it to your shop vac. The fine dust can quickly choke your vac, so clean the filter often.
With even a little experience, you'll cut an electrical box opening in less than one minute.
Drywall router with piloted bit
Operating a router
Mark the location of electrical boxes on the floor; shove wiring to the back of the box.
The usual set of tools needed for hanging drywall
Shove the wiring as far back as possible in the electrical box. Hang the sheet of drywall, but keep all fasteners about 16 inches away from the box so the wallboard won't crack when you make the cut. Mark the approximate centerpoint of the box and plunge the running bit at this mark.
Move the router to your right until you feel the bit contact the edge of the box. Tip the router slightly backward as you continue to move the tool about 1/4 inch to the right. This move jumps the bit over the edge of the electrical box. Return the router to its perpendicular position, and slide it slightly left until you feel the bit touch the outside of the box.