Agreeing with others who'd be more turned off by the heat than the hurricane risk. I went in January, plan to do the next one in January as well...and while January doesn't come with the risk of hurricanes in the Caribbean, it does come with the risk of getting snowed in on the way (flying from Montana, usually through Denver--between snow and the government shutdown I nearly didn't make it to Miami). I don't think there's any time that's completely without some kind of risk.
But, speaking as someone from a more northern climate, the weather in January was perfect. It was warm enough that I was out in t-shirts and capris the entire trip, but the only time I ever felt actually hot was the morning I went down into Cozumel. I've been to WDW in September, and that's as close to summer in Florida and the Caribbean as I want to get. I just about melt in that heat. I can deal with that somewhere like WDW where I'm moving around and going in and out of AC, but I wouldn't enjoy lounging around outdoors in that kind of heat, and while I enjoy the activities offered inside the ship, I wouldn't want to have to spend the entire trip indoors in order not to be miserable.