The ones I've worn look like this:

That's not a skydiving chute, it's an emergency escape chute, worn by aerobatic and test pilots in case they need to walk back to the airport. I'll never forget the first time I wore one, it was during spin lessons during instructor training. In shockingly few words this guy explained to me how to fly and land the tightly folded aircraft strapped to my back. The large silver handle here on this shoulder strap, pull it all the way out to deploy, look up, grab the loops, pull them down to your ears, pull left to go left pull right to go right, as you come in to land pull all the way down. I asked "Okay, how do you deploy the reserve chute?" He said "That IS the reserve chute. Plan A is landing the plane."

You wouldn't mistake it for a school backpack. It's not something you could easily hide under clothing without looking really strange.