here's something i learned from my butch husband and his buds who work on engines. it probably isnt real safe, but once in a blue moon probably isnt going to hurt you. i know it works like a charm.
USE SUPER GLUE.
clean the cut, let it bleed good, wrap it, all the good advice above. once it stops oozing squirt some superglue in there-it stings like a s.o.b.-and hold the flap in place with some paper towel or t.p. try not to stick yourself to yourself.

once it seals, carefully peel the towel away from the cut-some might stick to the outside but this will shower away- put on a finger cot and you're back in business. this will hold for the rest of the day unless you give it a really hard whack

-which you try not to do, of course.