I'd like to add some info from my one trip to Mexico. While I did catch an unusually large Striped Marlin out of Cabo, I released the fish, but I was privy to an incident at the airport that might save someone some grief. An older gent had a large cooler full of Dorado to bring back to the "States", packed in regular ice. Upon inspection by Mexican customs, he was informed that he could not airfreight a cooler packed with regular ice. Dry ice only!
I was able to watch this customs inspector wheel this guy's cooler out the main door of the airport, and literally, dump it in the gutter. The old man had a tear on his cheek, and it was a sad sight to see. It's not the U.S.A., and you can't argue with those people.
In most of the larger resort areas, you can buy coolers, and I believe that most resorts can supply you with dry ice.