When I go for a blood draw, I tell the phlebotomist, "I don't need a bandage, I'm not a bleeder. If I were I would have died long ago with all the cuts I get." I seldom go a week without at least one cut. I don't worry until the blood is spurting.
Heck, one time I was bowhunting and stabbed myself in an artery in the crook of my arm while trimming some brush. I held my arm up to my shoulder to stop the flow and continued hunting until the end of the day. Actually, I was more upset that I had just put a half inch slit in my new Goretex jacket. When I got home, I glued the cut with some Superglue and sew the slit in my jacket. I still have the jacket and it is my favorite outdoor jacket . I still have the scar as well. It is just below the site where they draw the blood.