If your pet is kept onboard your boat at all times, it's unlikely that you'll need to do anything. I haven't traveled in Central or South America so I can't guarantee this is the case there, but we have been to almost all of the eastern Caribbean islands. Our experience was consistent, no matter where we went. When we cleared in, we were asked if we had any animals aboard. We said yes, a cat, but that it would remain on board at all times. There was never any problem, and we were never asked for any type of health certificate.
It was a different story when we moved to our new home on Nevis. Since the cat was to be "imported" to the island, she had to have current shots, a vet health certificate, two separate rabies titer tests from the University of Kansas, and a sign-off from the US Department of Agriculture within 24 hours of the pet arriving on island. The government vet met us at the airport to check the cat, and we then had to quarantine her in our house for six weeks, with weekly visits by the vet. The fees for all this were considerable.