I take a first aid kit that I put together to meet the needs of someone who frequently hikes with newbies who won't carry stuff, and that matches my level of first aid training.

Wilderness first aid training should come first. Then everything in your backpack, and out of it, from trekking poles to pack frame, to tarp/tent fly, to clothing, to sleeping bag, clean water, etc are all a part of the "first aid kit" - and you have the ability to stabilize the person in distress with confidence.

I've never seen anyone carry an altoid can PSK such as you describe.