I've copied my response to your post in the Trip Advisor Forum here, to keep all the information together.
My husband and I have taken liveaboard trips to all of those destinations except
Honduras, but we have done land-based dive trips on
Roatan, Honduras.
The hurricane and storm season runs from June through November but you can encounter bad weather at any time of the year.
We also like to travel in the fall, primarily to celebrate our anniversary but also because the water is warm and it is the low season, so prices are down and popular
Caribbean travel destinations are less crowded; but we do run a higher risk of bad weather.
Below is a link to a site with historical information showing the frequency of tropical storms and hurricanes in the Caribbean. As you can see that the peak incidence of storms is in and around mid-September. But the Caribbean is a huge geographic area and a storm in one part of the region doesn't mean that the weather will be bad everywhere across the region. Although if a storm passes nearby you may get wind and waves and rain and poor visibility.
We tend to travel in late Oct and early November, again for our anniversary but also because it is nearing the end of the hurricane season - and we have been lucky over the years - but again there's no guarantees. We always buy trip insurance for a major vacation no matter what time of year we travel.
Of the sites that you mention above, my least favorite would be Honduras. There's not as much sea life and not as many large animals, in least not in my experience.
You are very likely to see sharks on
Bahamas dive trips and the reefs are very fishy, but the corals are not as nice as in some of the other Caribbean regions, again in my opinion.
You didn't include the Turks and Caicos in your list but you should. Beautiful reefs and walls, lots of sea life, and you are likely to see sharks and rays, including eagle rays, on just about every dive. Furthermore, the best T&C dive site IMO are French Caye and West Caicos, and they can be a little difficult to reach from the land-based dive ops on Provodenciales - you may spend most of the day on a day boat to dive 2-tanks. Therefore the best way to dive the T&Cs, again IMO, are from a liveaboard. One issue of possible concern is that the reefs tend to start deeper in the T&Cs, but not too deep and you can always stay near the top of the walls, but if you tend to use up air quickly, it is something to take into consideration.
We loved our trip on the Cayman Aggressor. It is an unusual trip because most of the sites you dive are accessible from land - but you get the opportunity to dive the best sites off of all 3 Cayman islands - including Little Cayman's Bloody Bay Wall and Jackson's Bight which rank among the best diving in the Caribbean IMO. Also the Russian Frigate off of
Cayman Brac which is an interesting and easy wreck dive and their are beautiful reefs and walls off Brac and GC, too. Many of the reefs start shallow in the Caymans and it you want to do a lot of diving in the Caymans, then a liveaboard is a good option.
However, the Aggressor will not make the crossing to the sister islands of Brac and Little if the weather is bad. We were on the Aggressor around the 3rd week of October and we had absolutely gorgeous weather and visibility and warm water. It was a fantastic trip, and we spent most of the time diving the BBW off LC, but we also got to dive the Russian wreck and lovely sites off of CB and GC, too. We also did an early morning dive at Sting Ray City that was so much fun. But the very next week the weather turned rainy and windy and the boat did not make the crossing. They only dived sites around GC and we heard that the diving was disappointing because of the weather - but that's always a risk.
The Cayman reefs are beautiful and there is much healthy sea life. You are likely to see some sharks but not many, but you will see other large animals, including lots of rays, turtles, eels, tarpons, groupers.
You don't mention budget, but if that is an issue of concern, you might also want to look at the Caribbean Explorer's Saba trip. The boat is nice but a little smaller and older. I don't remember lots of large animals but lovely corals and abundant sea life, and diving the sea mounts around
Saba is unique and interesting. And you a;so get the chance to visit 3 different Caribbean islands. On our trip we embarked from St. Martin, traveled to St. Kitts, and then to Saba - and they offered some optional shore excursions which were great.
There are lots of great liveaboard dive opportunities in the Caribbean, I hope that you have a great trip!
Hurricanes and Storms