Ahem! The local Medical Expert here lol. Anyway being a nurse in my day job. I would not worry too much about the dark red blood from your facial area. Your correct about the brighter the blood the richer in O2.
The reason for the darker color is it depends on where on your face you cut yourself. Blood travels over capillaries, Vessels, Arties(you would be in some serious dodo if you cut this one lol) but each of them have a certain function. One carries blood to the body parts ie very bright blood and then those that carry blood away from organs back to the lungs to be oxygenated and back to organs again.
Now if it was green your a Vulcan.