Weapons on board the Ship are many and varied. If you can pick up an object, you can probably also use it as a weapon. Use your intuition here, for example a knife is obviously a good weapon whereas a top hat is probably not.

Bludgeoning
There are a number of bludgeoning weapons on board ranging from hammers to mannequin arms and tennis rackets.

Stabbing
Take a look around for knives, katanas, letter openers and other stabbing weapons.

Firearms
Guns are harder to find but some of the crew and passengers do have firearms on board. If you can find the armoury you'll find a host of weapons at your disposal. The flare gun on deck can have an interesting effect on your quarry too...

Poison
You can poison your Quarry if you can find the right method. Oh, and where the poison might be stored... The doctor's office is often a good place to look.

Environmental Traps & Triggers
Some locations on board are quite lethal if you can just catch your Quarry there. Try the freezer or the sauna. Or why not drop a lifeboat on their head?

Other
There are a number of other more bizarre ways to dispatch your quarry if you can find them...