I wonder what scale you have to produce satellites at for the raw material to be a price driver. Satellite development is very expensive, just the material of the structure is probably a rounding error compared to the total cost. How much would you save by using wood there? Even at Starlink scale, I would be surprised if it’s worth it.
My guess is that wood will splinter on impact in a way that metal does not. A flake of old paint in orbit will turn this cubesat into hundreds of satellite killing splinters. Those splinters will do untold damage to other satellites.