This doesn't happen all that often, but it can happen. It will usually happen during the fall months, as this is the height of hurricane season. I don't have any hard numbers, but I would venture to guess that it happens 3 or 4 times per ship per year, probably less.
It happened to us on an eastern 7-day in October of 2000. There was a hurricane in the southern Atlantic heading towards the leeward islands, so we stopped at Key West on the first day. There was also talk of a stop at Nassau and an extra Castaway Cay call, but as we pulled out of Key West, the captain announced that we were heading for St. Thomas, as the storm had turned south and been downgraded. So our itinerary ended up being:
Sat. - embarkation
Sun. - Key West
Mon & Tue - at sea
Wed. - St. Thomas
Thur. - at sea
Fri. - Castaway Cay
In the end, we swapped St. Maarten for Key West. I actually enjoyed the change of pace. The only rain we saw on the entire trip was during the first night and early morning at Key West.
Recently, the port of Georgetown, Grand Cayman was closed due to high seas, and the Magic had to skip its call there. It instead called early at Cozumel and remained there for an extra half day, I think. Since Georgetown is a tender port, the rough seas make it hard to work the tenders from the ships at anchor to the shore. For other ports, with cruise ship piers, there would have to be pretty substantial wind and sea conditions to keep the ship from docking.
I've also heard of Bahamas cruises substituting a day at sea for a Nassau or Freeport stop. The Wonder once called at Charleston, S.C. due to a hurricane in the Bahamas.
While the weather is hard to predict at any time of year, I would think that you will not have any problems in April. It is not during hurricane season, and the weather is generally very warm in the Caribbean at that time of year. My advice would be to not spend a great deal of time worrying about this. I think it's unlikely that it will be an issue.