Actually, stone shot is about as effective against wooden ships as cast iron shot, as the lighter weight is compensated by having a higher velocity, and at the short ranges of early naval battles, loss of velocity was rarely a factor. The Carronade, used extensively during the Napoleonic Wars, also had a low velocity shot, but when you are typically engaging at ranges of 100 yards or less, the difference in effect on the target was minimal. The real problem with stone shot, as discussed by John Guilmartin in his classic work, "Gunpowder and Galleys", is the cost of producing the shot, as each one had to be manually shaped into a sphere of a given diameter, which was manpower intensive, and if you paid the workers, expensive.
Ballistics Discussion for the Really Hard Core
When a cast iron roundshot hits a wooden hole at a reasonably high velocity, it tends to simply "punch" through, leaving a slightly larger than caliber-sized hole, and expending its remaining energy behind the outer hull. If the shot penetrates the gun deck and happens to hit either a gun carriage or gun barrel, that energy is expended on the gun deck, to the detriment of the sailors manning the guns. Obviously, any sailor hit by the shot is probably not going to be around any longer. However, if the shot does not hit something, it is very likely going to either bury itself in the hull on the opposite side of the ship, or if the range is very short, simply punch another hole on exiting the hull.
When a large caliber, slow-moving shot, such as a 32 to 68 pound carronade shot, or a stone shot of lighter weight for a given diameter, hit a wooden hull, the effect is different. Much more of the energy of the impact is transferred to the wooden hull, resulting in a much larger hole, and a great number of wooden splinters. Most of the casualties in a naval engagement during the Age of Sail were caused by those wooden splinters flying about in a high velocity cloud. Since the shot lost most of its energy smashing through the hull, it also has a greater tendency to bounce around inside the ship, wreaking more havoc. The 68 pound Carronade was not called the "Smasher" by the British navy for nothing, but the large shot was hard to handle and load easily.
For an example of the difference in damage between shot fired from long guns and shot fired from large-bore carronades of equal weight (in terms of cannon barrel weight, not shot weight), compare the results of the combat between the USS Ranger, under John Paul Jones, and HMS Drake in the American Revolutionary War, and the combats between various US Navy sloops and Royal Navy brigs during the War of 1812. The Drake's bulwarks were described as being shattered, but her hull was not seriously damaged. In the combats during the War of 1812, the US ships on a regular basis sank their opponents. The difference lies in the nature of the armament: light, long guns verses large-bore carronades.
The problem of a ship with an all or almost all carronade armament is that if it encounters a ship carrying an armament of mainly long guns, that is also able to chose the engagement distance, is that the ship with the short-range carronades can be shot to pieces by the ship with the long guns, as exemplified by the engagement during the US War of 1812 between the USS Essex, equipped with forty 32-pound carronades and six 12 pound long guns, verses the HMS Phoebe, carrying twenty-six 18 pound long guns, as well as upper deck carronades.