Is it just the B tuner that is out of position? Check them all just in case as sometimes the headstocks can be 'slightly' asymmetrical.

If you are careful (and if the tuner's washer will hide the plug) you may be able to preserve the finish and not have to sand at all... if you pre-cut your dowel to length (ie headstock thickness) and sand the ends before gluing it. Then, use a low tack masking tape to mask up over front and back of the hole, cut the tape out of the holes, make sure the hole is free of finish/TO, then glue with Titebond and clamp front and back to ensure it's flush. Remove the clamp and tape after an hour or so then give it 24hrs to set completely. Measure, mark and spike (so the bit doesn't wander) the position of the new hole, re-drill and hopefully you'll be good to go.