Not a trick question, but a real puzzler - which spacecraft or spacecrafts incorporated real wood structural elements?
I think that Soyuz launcher uses wooden parts in engine ignition process (proof link in Russian: https://geektimes.ru/post/273782/)
In the mid 1970's China had a series of reconnaissance satellites called Fanhui Shi Weixing (FSW). These were designed pretty early on. They were recoverable and mostly used for mapping and internal geography of China. They were recoverable because at first they had film cameras like early American spy satellites. These had a heat shield make of white oak. It apparently worked well since there were quite a few, (20 something?) missions. Later on they tried to evolve them into manned spacecraft. In the west it was believed they had a failure causing the loss of the astronaut, so that program was discontinued. I believe FSW (with improvements) were used again for reconnaissance. Later they got people up in the Shenzhou program.
A wooden Space Shuttle?
Before the Space Shuttle ever flew, a lot of testing had to be done. Among the test items were the OV-101 (Enterprise), STA-099 (later OV-099, Challenger) and the Pathfinder (later OV-098, no STA designation known). The latter was partly built of wood.
The Enterprise was built without engines or functional heat shield. Also a lot of other systems were missing. It was intended as a flight test article first, but was planned to be upgraded to full orbiter status after conclusion of testing, becoming the second orbiter after OV-102 Columbia. Design changes during the construction of Columbia forced NASA to reconsider this. After the Challenger disaster, refitting Enterprise was again brought up but ultimately decided against.
Like the Enterprise, Challenger was first built for testing. It was a full airframe with a mockup crew module and partial heat shielding. It was put to the test for 11 months. After that it was fitted with a functional crew module, parts were reworked and was launched on orbital missions as OV-099.
Space Shuttle Pathfinder (retroactively/honorarily assigned number OV-098) was another full sized orbiter test article, but built out of steel and wood. It was mainly used for testing all shuttle ground facilities: cranes, roadways and other heavy equipment. It completed 6 missions, but zero of those actually went into space. It was later refurbished into a fully equipped model using a test tank (MPTA-ET) and two prototype Advanced Solid Rocket Booster casings.