OY! So much with the advice from people with no knowledge. You're going to be just fine. Just understand that the locals don't regard dogs as members of their family...more like livestock. So PLEASE keep him on a leash on Tortola, VG, and JVD. Poison is common, particularly on JVD.
It will be a great experience for all of you! Just be sure that you give him a freshwater rinse EVERY night, whether he's been swimming or not. And dry him with towels. The salt interferes with his natural ability to cool.
You will be well-received by all ex-pat establishments. You will be well tolerated by local establishments.
EVERYONE will be anxious to welcome a well-behaved, friendly pup.
In an abundance of caution, you might touch base with Dr. Sarah, just in case there's a need.
Have fun! Please report back on your experience!