Okay, you do not want to pry on the wood if it is held on with screws. My observation was that on American-made cars, dashboard trim is generally glued on.
They do things differently in Sindelfingen.
I suppose a really thin craft saw might be used to saw through the screws, but then you would need to get new screws and removing the old ones, which you will have beheaded, might be a chore akin to removing the tick's head from your Blue Tick Hound and therefore quieter, but no less unwise.
I apologize and hope my advice did not ruin anything.
Semibodacious Transmogrifications a Specialty
1990 300D 2.5 Turbo sedan 171K (Rudolf)
1985 300D Turbo TD Wagon 219K (Remuda)
"Time flies like and arrow, yet fruit flies like a banana"