The Boy Scout Permit is more of a "travel permit"----they have never been too specific on what trails you are hiking. I have been a Scoutmaster for 6+ years, and mostly the Scout Office is looking for car insurance, trained adults, seatbelts for the scouts while traveling, etc. I have never had any pushback on the "exact" trail we are hiking. Just simply put "hiking trailhead in Whitney area, either Whitney Portal or Cottonwood", etc., and you will be fine.
Have fun---I did this hike 2 years ago with our scouts, and they had a great time. We went from Horseshoe Meadows around the West side and summited Whitney, and then out through the MMWT. It was a great trip, and the scouts still talk about it today. We had 2 12 year olds and 1 13 year old. We hike quite a bit as a troop, and they had no problems whatsoever.