Back in the days when shaving was done with a razor blade rather than an electric shaver, every medicine chest held a styptic pencil. I hadn't thought of them in years until today when a friend's dog had a foot pad bleeding. Now that I've remembered them, I need to get a couple for my medicine box. I have compresses (bandages) for more profuse bleeding, but the pencils sure would be handy for smaller cuts and nicks.
If you aren't familiar with styptic pencils, they are a stick of compound you put on a cut that causes the bleeding to stop. The common ones are usually anhydrous aluminum sulfate (alum) or titanium dioxide, and they cause the blood vessels to contract (think pucker!) which slows or stops the bleeding. You can see a picture of one here.
If you own a cat or dog and cut their nails, you probably have a styptic powder on hand in the event you clip a nail too closely, causing bleeding. It would be good to have a styptic pencil on hand for your own cuts.
Styptic pencils are very cheap. Amazon carries one for under $2; they don't go bad as far as I remember, so I think I'll get several.