You'll probably have to go boondocking. Any official provincial campground, recreation site or Hydro campground will be a no shooting area.
That said, when camping around Harrison lake I've heard my fair share of gunshots (and bear bangers) and I've seen signs of .22 shots and the occasional 9mm on signs. Lots of helmetless yahoos on ATVs up there too. It's been a while since I went up there now. It was a long FSR up the west side of Harrison to a Rec Site. The road washed out a while back and I think a landslide caused a mini tsunami that washed out half the campground, so I don't know if it's there anymore.
You can try the iOverlander app to find boondocking spots. You'll want to try to get way up an FSR and away from civvies. You'll probably scare the shit out of any couples or lone campers up there on their own, even if you don't think they should have anything to fear.
And please, please don't combine shooting with booze, and shoot into the mountain.