Been there, done that. Now, I carry a couple of bandaids, folded in half, in my wallet. It's
obviously not a complete first aid solution, but they have kept me from getting blood
everywhere on more than one occasion. :-)

For me, a bandaid is more than just a way to keep dirt out and blood in. It also prevents
the little flap of skin you get with shallow angle cuts from catching on everything.
I *hate* that. A cut that's not serious can still be annoying and distracting.