I hate when people in movies need to make themselves bleed, so they cut open their palms. Excuse me?! You’re gonna need that! You’ve got blood everywhere and there are way easier places to bandage. Don’t injure the single part of your body you are capable of holding a weapon with.
You also have a lot of areas with less pain sensors, which are going to be less likely to pull themselves back open due to being moved.
Try your damn forearm. Or your scalp if you need a lot of blood.