I don't have much good news for you. According to Freighter Trips (and various other sites I could find):
Many people who are taking a freighter voyage as part of a long term
stay abroad, or a permanent relocation, ask about the possibility of
taking their pet with them.
For animal lovers, this would certainly be a dream solution to their
relocation problems, but sadly I believe it is now impossible.
Freighter shipping lines will not allow pets to stay in a passengers
cabin, or anywhere else onboard ship.
The only transatlantic cruise ship that seems to accept dogs is the QM2
The Queen Mary 2 operated by Cunard Lines is an approved carrier in
connection with the Pet Travel Scheme (PETS) on Transatlantic
Crossings. Passage in the kennels is subject to size restrictions,
availability and the requirements of the Pet Scheme. Pets are accepted
on all Transatlantic crossings, except the first and last crossings of
However, that goes from Southampton to New York. You'd have to get to the UK and then drive down the US and cross from perhaps from Key West or somewhere else in Florida.
For air travel, you can do Tenerife to St. Lucia or Barbados via one stop in London Gatwick which doesn't sound too bad if you get appropriate advice from your vet.
There is at least one cruise ship that travels from The Canaries to the Carribean but like all the other cruise ships except QM2, they only allow service dogs.