In June you are in the hurricane
period, albeit at the beginning and far from the early September statistical height of the season. I would take my time going the route
from BVI-St. Martin and then taking your southerly route by island hopping as your inclinations allow. Just keep up on the weather
and be prepared for a (motoring) sprint down-island to get below the projected track of any depressions that might form. The winds will be light at that time of year, so you should ensure that you have sufficient fuel
a significant part of the way.