Your biggest risk on a cruise during a hurricane is missing some or all of your scheduled ports of call. This happened to us during Hurricane Jose last year on a Windstar Cruise. We missed three scheduled ports, including the two I had specifically booked the cruise to visit.
For two ports, they were able to substitute Grenada (a delight) and St. Lucia (also nice, but we had been there before), and they gave us a $25 per person credit for the final missed port. The change of plans was disappointing, but we made the best of it and had a great time anyway.
We sailed far enough away from the storm that weather and seasickness were never a factor, even on such a small ship.
If you have your heart set on a specific itinerary, you might want to celebrate your anniversary earlier or later. Though the hurricane season officially lasts from June 1-November 30, the peak months are usually August and September. Good luck.