Depending on how early you wake up, you should be docked already when you wake up in the morning.
I don't have my navigators from last week with me, but I want to say you don't leave Key West until around 9 or 10 pm, and you don't leave Cozumel until 10:30 pm.
In my opinion, you have MORE than enough time in Key West (unless you are an avid shopper), but you can easily use all the time in Cozumel, and still not have sctratched the surface. It is one great port.