There is really no way to speed up the healing process, but if you just cut and still have a week before you go on vacation and it really is not too deep as you say then you should be almost fully healed by then. The body heals quite rapidly, banning any abnormal healing problems such as diabeties, or a blood disorder. I would not worry much. It will pretty much be a scar by then, although probably not a faint one.
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