Hurricane Season In Cayman is Officially June 1st to October 31st, however we don't tend to get any until lat eJuly .. but it carries on to November for us.
Now that being said we only tend to get the odd tropical storm near by, and maybe one or two hurricanes (normally cat 1) coming about 180 miles of us by the east coast from south to north. The worst ones historically are late october or november.
I personally would say that you are better off staying land based and if you want to do all three islands fly there and do them, the aggressor takes as much time as no fly time take to get there anyway, they just travel over night.
As Alex pointed out it is often that the aggressor gets stuck on one side of Grand Cayman, which is not a bad thing until you are on the aggressor. The reason this is bad is the aggressor needs special moorings to tie off to (no anchor dropping allowed in Cayman) and each side of the island has maybe 5 dive sites for the aggressor to use, which means you could be stuck on 5 sites for a week instead of three islands, where as if you were land based even if the weather turns bad you still have about 50 dive sites to choose from.
If you are worried about price It would be interesting to compare Agressor to Land based, I have never done that, You will find you won't have to lug your equipment around very far most companies pick you up at your door, and you just have to carry stuff onto the boat from the car, which parks by the dock or beach you are going to.
When is your trip wanting to go as time of year around here can factor in a lot of variants for the trip too .. like in October there is Cayman Madness And september is low season and so much cheaper (and can be the best weather too) .. also time of year brings about diff sun positions for photography, and different wildlife in the water too. If you want to get scientific about it you could spend ages planning a trip, if you know you want a liveaboard and are not bothered by anything else then you have the choice of the Agressor. If you want to go land based you have more dive operators to choose from that you can count, all offering something slightly different, and some different sides of the island, some have small boats, some cater for photography, so have big boats and take lots of people ... it's a tough choice.
If you want some further information, feel free to ask me, If i have time to help I will, I live here, and have worked for a few companies on the island, and know most of them and the people who own and run them, so I can advise you for what you want, but like i said if you know you want a liveaboard for the ease and conveniece that some people like in that then just contact the aggressor.
enjoy your 50th
Giles