I'd get some Aquaphor ointment at the drugstore and keep the cut area really clean and covered w/ the ointment--it aids healing and reduces any potential for a "bump" from the cut. Less than a week you should be able to clean it up with a razor unless you really gouged it out. Learned about this stuff early on in my experience w/ skin cancer and precancerous removals. Great stuff. Just wash with a mild antibacterial soap then spread a thin layer a couple of times a day. Good luck.
I usually shave around the affected area, and then go over that spot -- very carefully -- with an electric razor, until it's healed enough to withstand the blade again.