On Earth, if a ship in the Age of Sail has weapons, it has cannon, which requires gunpowder, which in turn means our world almost certainly has guns. If we don’t want guns on our fantasy world, then no cannons either. That means a ship with no fire power and hence a lack of drama. Where’s the fun in that? We can either keep the cannons or replace them, the latter requiring some understanding of what we’re replacing. We’ll need some details on how fast cannons fire, how far, and how many people are needed to do this. Then we can consider alternatives. For example, wizards may provide an equivalent to gunpowder, but if that alternative exists in enough quantity for cannons to exist, then wouldn’t guns, too?
A 36-pounder, meaning a cannon that fires balls weighing thirty-six pounds, is among the largest cannon aboard ships and requires fourteen men. A powder boy brings gunpowder from below decks; gunpowder is wisely stored somewhere less prone to explosions. This role is eliminated in a world without gunpowder. If we invent an alternative to the cannon, and there are a hundred such weapons, we’d have a hundred fewer crew aboard, which in turn reduces supplies needed.
A chief gunner aims the gun and primes it for firing, but does not fire the cannon; one of the other gunners does this. This role would still require an alternative, but the role would likely need a different name. The chief gunner is in charge of the crew, who practice together but seldom do so with live shot due to the cost. Not practicing with live shot affects the chief gunner’s ability to practice aiming, but the rest of the crew can at least become efficient, affecting speed of firing, which is two to three shots in about five minutes.
The rest of the men are called gunners. Some gunners prepare the cannon for firing, as follows. One gunner shoves a wet cloth down the barrel between shots to put out any sparks before more gunpowder is loaded. One man inserts a cannonball while another rams it in. This is followed by another wet cloth wad to prevent the ball from rolling out if the cannon is aimed downward. These various details and personnel are specific to the firing of a cannon and might be replaced by a different number of personnel depending on what replacement weapon we devise.
Cannons require men whose primary job is moving the cannon back and forth. Prior to firing, it must be pulled away from the hull because it is loaded from the barrel, but must be fired with the barrel protruding from the hull. This means men pull the cannon back, several people perform various loading operations, and then the cannon is shoved against the hull before firing. Cannons have huge recoil, meaning they leap backwards when fired. This means several crew are needed to shove the thing back into place. We might not need these men with an alternative weapon that lacks recoil.
Smaller cannons still have the powder boy, chief gunner, and at least two other gunners for cleaning, loading, moving, and firing a cannon, so the number of men depends on cannon size due to how heavy it is to move around between shots.