I know you were being facetious, but helicopters have a surprisingly low operational ceiling. Google suggests 10,400 feet for hovering, which ain’t much for a rescue helicopter in high mountains, Everest base camp for example is at 17,500 feet.
Yeah, but that’s hovering. I’m not saying it is easy, but you can go up higher with a helo. MI-8 can fly slow at 4000m and people have jumped from helicopters _over_ Everest and landed at basecamp. Maybe still not high enough for someone armed with a long pointy stick to poke a balloon, but close.
Maybe they need another balloon and some people throwing darts at the first one from above.
Hmmm, what if they miss? Ok, darts with small parachutes. Lawn darts.