Several times I have sliced a finger with sharp knives and not had time to go to ER and have it stitched. I find that five or six bandaids at once, changed frequently, will usually stop the bleeding in an hour or so.
I fell while skiing two years ago, twisting my knee when the ski got caught under about a foot of new snow. The loud screams brought my daughter running (or skiing), and I managed to extricate my foot. The pain pretty much stopped then, so I tried another run. Bad idea. I now wear an elastic brace full time.
Several years back, when my daughter was eleven, she and Daddy were skiing in a wilderness area near Lake Tahoe, and stayed overnight at a Sierra Club hut, where they were the only tenants. When they left the next morning, Daddy managed to slam the door on his little finger, cutting off part of the tip with the sharp edge of the door jamb. Sarah wrapped it up, and then they skiied several miles back to the trailhead, and drove to the local hospital to get it tended. When they came out of ER, he found that he had left the headlights on and had to jump-start the car. When they got home that night, they were both laughing hysterically, telling me the story. Sarah was especially charmed at the idea that when the next person opened the door of the ski hut, a piece of Daddy's finger would fall out.