I just saw on that Dr. Something day time show (I forget what it's called at the moment), that leaving cuts unwrapped is a common mistake made by even doctors often. He said you should always wrap with plenty of neosporin. Leaving cuts wrapped to form their own covering (scabs) actually makes them bigger and take longer to fully heal. I would say to avoid infection, just clean and rewrap often.
So cleaning.. neosporin, then bandaid? Alright then!