Based on the issues of wood expansion with my clocks, a natural project would seem to be a wooden hygrometer. At least, it ought to respond about as fast as the wood in the clocks responds, which appears to be around a few days.
The design is fairly simple, with two oak sticks of roughly the same length being placed parallel to each other and rigidly anchored at one end. One of the strips has the grain running lengthwise, while the other has the grain running perpendicular to that. The two free ends are pinned to a needle. I placed the parallel-grain strip on the bottom, so that the needle moves to the right as the humidity increases. With this particular item, fully soaking it for a week in water runs the needle all the way to the right of the scale.
But the typical indoor humidity is closer to the first picture. The needle usually moves around 1/4"-1/2" with daily variations.