Also, there is no way for me to go directly to sea without first getting to ship deck. Fast travel has no such option.
You don't need to use fast travel, especially if you're on a shore and the boat is just a short distance away. Walk to the boat (or to the dock if you're in a port), then you should get an icon to board. Press "Enter", and you should get the option to go straight to sea.
However, I think I've solved the problem. Before giving you the report, the quest has to check that you're on the right island - we can't have you taking a mission from the governor of Port Royale and then smuggling the stuff to Cayman, can we?
There are two ways for code to figure out which island you're on, and it turns out that only one of them gets it right when you're on a ship's deck. Unfortunately I used the wrong one.
Put the attached file into "PROGRAM\QUESTS", then you should get the report when you go to your deck.
Unless I'm only using the governor for that safe pass in case I get busted one day, no?
But now that you've mentioned that killing them would get me a better reward, I might try to deliberately get busted then. Will this ruin my relationship for the smugglers just on that colony or for the entire Caribbean? Because if it's the latter, I'd rather keep dealing with them.
You don't keep the pass. If you show it to the coastguard then they take it. If you don't, the governor takes it when you return to report on your mission.
Provided you kill all the smugglers, the guild does not hate you at once. They know something went wrong with the deal but with no witnesses, they don't know what you did - for all they know, the gang was attacked by coastguards or a rival gang. If you keep doing it, they'll get suspicious and eventually block you.
Once you're blocked, it's for the whole Caribbean. But the smugglers' guild puts profit before permanent grudges. The next time you talk to an agent in a tavern, he says that you're blocked but that he'll lift the block for a price. Pay him, then arrange the deal - and then arrest and kill the smugglers again.
(Arresting smugglers during a governor quest isn't the only way to upset the guild. Doing the "Smuggling for Thomas O'Reily" sidequest and choosing to help Thomas rather than chicken out when you meet the gang on Rocky Shore will also make them hate you.)