Shipwrecks in Black Forest and Swamp yield a lot of fine wood, but they are at least uncommon if not rare. They can be found in shallow water, so coasts, rivers, and watery swamp areas. Destroy them with a weapon.

The towers with a wooden roof and a lot of dwarfs outside, in Black Forest, always have a wooden stool you can destroy to get 1 fine wood. Likewise, some of the towers have a table and a bench inside, which you can also destroy to get fine wood. Some Swamp cabins also have furniture.

Trees are the most reliable method, by far, though. My current world seems to have a lot of shipwrecks but that is just good RNG and nothing to rely on.