For minor cuts, either apply a bandaid or do nothing. Carry tape, moleskin, or donuts for blisters, a very common problem. For splinters and cactus spines, I usually just leave them in and let them leave on their own schedule.

I have been on trips where every elastic bandage, about sxc in all, was pressed into service holding various knees and ankles together.

My basic kit is an elastic bandage or two, along with some decently large (4x4) dressings for big stuff, tape, assorted pills, safety pins, and barrier gloves. Splints are easily improvised, although I occasionally carry a SAM splint. Many items commonly carried have uses in first aid. On one occasion we had to fashion a cervical collar from a part of a foam pad for an individual suffering from a rock right in the head which destroyed his climbing helmet, but which did its job and saved his noggin.

More of your gear comes into play as you stabilize the victim, keeping him/her warm, and ready for transport. You may need to build shelter and fire up the stove. Having a signal mirror/strong light can come in handy for helping the helicopter find you, although we have built a fire for the same purpose. If things get complex, just about all your outdoor skills can be involved. Its knowledge, not so much gadgets, that is really necessary.