Most concepts for VS2 ship addons have weaponry that fits in with the design of the addon. This was not originally considered for Eureka, as it is meant to be basically a direct port of older style moving block mods. However, a probably cause for older style moving block mods not having these weaponries is a lack of technical capability for ships to conduct combat, i.e. be damaged, have combative crew, etc.

Additionally, most other VS2 addon concepts split weaponry between anti-personnel and artillery, to simplify the vast and complex world of naval warfare down to a more Minecraft reasonable standard. However, adding more than one or two ship weapons will go too far out of scope for Eureka, pushing more into the territory of the Melodious concept.
For consideration: Instead of a cannon, which would be good for ship v ship, or a harpoon, which would be good for ship v player, I'd like to propose adapting the already vanilla Crossbow.

Historically, early ship weaponry was in the form of mounted crossbows, such as the Roman Ballistae. In vanilla Minecraft, the crossbow is a powerful PVP tool, capable of using arrows, potion tipped arrows, and fireworks. We can adapt this gameplay to ship design to allow for a vanilla friendly ship weapon that is easy to understand and fits with existing design concepts.

The Mounted Crossbow is a turreted weapon. Right clicking on the empty crossbow with ammunition in your hand (arrows or fireworks) will load it, and the weapon will load as fast as a vanilla non-enchanted crossbow. Right clicking or using a redstone signal on a loaded crossbow will fire the crossbow. Shift right clicking on the crossbow will aim it to the direction the player is facing. The mounted crossbow is designed to not be automated, and should not have any autoloading capability. The redstone capabilities should be able to be activated by a constant signal, not just a pulse, such that a player can stand on a pressure plate behind the firing crossbow and continue to load it for rapid firing.

A necessary change to facilitate this weapon is fireworks damaging blocks. To this end, I propose that mounted crossbows should be crafted with additional reinforcement, allowing it to fire harder. Arrows will shoot further, and fireworks will pierce blocks. This still leads to TNT cannons being worth constructing for larger blast radii, and solves some of the issue of the relatively short range of pvp engagements compared to what a naval engagement might be.