We went last year both in June (3rd-) and December.
June was a bit tougher because the heat and humidity really made everything a bit harder. The daytime sun sometimes felt a bit unforgiving (hard to be completely covered in sunscreen) and sleeping in 25+ degrees was a bit sweaty
It's quite bearable, though, and I would go again in June any time!
Looking at historical
weather, June has more rain than both May and July. We had some as well, but it was really quite refreshing.
Most of the tropical storms (if any) arrive in the fall, so the
hurricane risk in June was very much downplayed by the
charter company. Their boats were fully booked through summer so I guess their customers agree.
So, a wonderful place from April to June, I'd say, but the weather actually might be somewhat more inhabitable in April-May. You're not chartering but if you would, their discounts usually start from June