I've not been to the Caribbean in Jun/Jul, but I have frequently been to the Bahamas out islands then. Warmer and calmer. I've not personally been threatened by a tropical storm, nor hurricane, both of which would seriously ruin a vacation.
Let's look at the facts. On average, there are 10 tropical storms and 6 hurricanes each year, or 16 in total. Between the two combined
, you are going to see just under 2 per year in June and July combined, with July being just a slight bit higher than June.
TCFAQ E17) How many hurricanes have there been in each month?
That's roughly 1 storm in each month, but that doesn't mean they will hit the BVI, or necessarily come close. The odds are well in your favor.
By far, September is the most active month, with 6, followed by August, with 4.
Of course, Emily was a category 5 hurricane that went through the Caribbean in mid-July 2005. It happens. It had to ruin some vacations in the BVI, even though it's track was south of BVI. It formed only 3 or 4 days before it hit, but you would never know for sure in that time frame what it was going to do. No doubt, you would want out.
If I knew I could get out, I would go.