In my magical world, for reasons magical, metals such as iron have never gotten used, and even use of bronze is scarce. On the other hand, magic allowed for refinement of wood, similar to the densified wood, although the material produced isn't as strong as the densified wood, but is still a lot stronger than regular treated wood used for 16-18th century ships.
Well, this leads to some problems that I need to address for my naval battle to feel realistic. Let me explain the situation. We have setting of civilizations, whose development outside of magical advantages is similar to 15th-17th century.
A large isolated empire has recently ended their isolation and sends one of their fleets of ships that are quite long (longest being 156 m long flagship, but other large ships being at least 100 m in length and core medium sized ships still being around 70 m long) but somewhat less armoured against a small island country. These ships have been built for battles that focus on archery and short ranged (<200 m range) fire magic. Recently, they've also developed magical cannons.
Most of their ships simply have 2-3 magic cannons in front, and only their flagship actually has almost broadside design with 12 magic cannons (magic cannons are hard to make, so they use 1 front facing cannon and 11 cannons on single side, with addition of forecastle and aftcastle for archers and magic flame throwing weapons).
Small island country they're attacking is behind on magic technology, but way ahead on naval cannon tactics, as they have started using magically-hardened-wooden black powder cannons and have been working on naval cannon ships for some 80 years by now. They have already developed ships of the line, and while their navy is small, with only some twenty large warships and thirty frigates, their ships are built to at least somewhat withstand their own atrillery.
Important advantage of a magical cannons for this scenarion is that it uses magic force transfer, rather than explosion, to propel the cannonball, and thus it can easily fire 38.5 pounds (18.5 kg) cannonballs (which, however, are made of granite[because no iron] and thus are size of the iron balls of 110 pounder), but it only has around 350-375 m/s muzzle velocity.
On the other hand, wooden cannons of the islanders fire 11 and 24 pound (granite) cannonballs (which are the size of 32 and 68 pounder calibre iron cannonballs) with 400-425 m/s muzzle velocity.
While I do have multiple other problems I need to solve for this battle, my current most important question is, how do I make sure whether these guns are good enough to substantially damage enemy ships, or taking in account magically hardened wood, are able to damage the ships at all?
Edit: Reason I didn't assign specific value to the wood hardness is because that is, sort of, what I am looking for. I need a way to decide how hard the wood should be for existence of cannons to still be reasonable. My goal is for hardened wood to be reasonably more resistant than wood, (equal to at least 2-3 times thickness of regularly non-magically treated wood for things like shield). If that is impossible, I might have to adjust cannons calibre to make it possible. I am looking for some general advice on how to approach this problem, or alternatively numbers for real life black powder cannons vs wood penetration, so that I have some framework to work with.