How much drywall should I cut to re-route some wires?
Unless you have scrap laying around, you'll be buying a 4x8 sheet of drywall anyway (unless you can find damaged panels or the hardware store sells half sheets).  So anything less than 4x8 will be about the same amount of work to patch, so cut out as much as you need. Just remember to try and end in the middle of a stud.  

If it's 8ft. from floor to ceiling, cutting out all the way to the next stud would mean you'd only have to tape one seam. This would likely be easier than patching a bunch of holes.