Actually, that't the guy who can and probably will simply hoist you up on a coat peg and leave you helplessly struggling like an idiot. The big guys don't HAVE to be mean. They can afford to just humiliate you. It's more fun and has fewer consequences. I'm kind of a big guy myself (6'4" and solid), and I don't get into bar fights. When a drunk starts getting loud and pushy, I just quietly say, "Don't get stupid," or words or a look to that effect. My days of having to prove anything are far in the past. If you're looking to die, go after the short biker with the crazy eyes. He's the one who'll finish the job.
Ability to kill a man, specially cold blooded type using guns, don't depend on the physical built of a person. It's in the mind. Ask a policeman or a marine.
You do not have to describe every gory detail. If someone puts a gun in their mouth and pulls the trigger; well yes there would be one heck of a mess, but as a writer it is not necessary to describe it. Give your reader some credit, they will get the message.
I feel the gun option isn't being looked at from every angle. Yes, when you think of suicide by gun, most of the time the wound is to the head -- but there are times when someone shoots their heart. Therefore, a simple solution and without the brains. Ah, guns. You are the cause of and solution to many of life's problems.
If a character really wants to die, they won't worry about being found. The only ones wanting to be found are the ones who want someone else to either catch them in the act and talk them out of it, or catch them before the actually die and save them. It is all an attention scheme of the emotionally distraught at that point. If the character is actually suicidal and doesn't care about being found, but you as the writer want him found as part of the plot, well then that is another matter. You could simply have a crewman see him jump overboard, but alas, the crew could get to him in time to prevent his drowning.
If it's a vessel with masts, hanging. It's dramatic, he'll definitely be found and there's the awkward conversation looking up at him or with his feet right about their head level during discovery. If it isn't a long drop you can get in some twitching and jerking if he's found quickly. If he isn't found quickly there's the sort of oddly peaceful but very creepy notion of him swaying with the movement of the waves, like part of the ship. A more sensitive direct character can stay his sway by grabbing his ankles while directing another to cut him down and this can be used to further the character development. A refusal to look up at the body, or another's casual shrug can be used. This can be a major scene with a lot there.
Why not go with something unconventional, such as water intoxication? Drinking only salt water would be another easy way to go.
A period piece on a ship? Pirates try to take the ship. He charges on their ship and starts setting fire or trying to kill as many as possible. Perhaps try to destroy their helm to make it more difficult for them to follow the ship he was on. They kill him. Suicide by pirates. Heroic death. Distraction gives his ship a chance to escape.
I have two ideas based on the little insight I have on the character. One, he comes to a decision to shoot himself, ingest poison or whatnot but at the last minute has a vision and finds a reason to stay alive, he goes back to the deck and is killed by say a stray shot, a violent wave throws him overboard, a gunpowder barrel ignites, something ironic if you catch my drift. The other idea was if piece is set in a time when ships had crude engines maybe he could simply throw himself into the furnace or boiler.