There are quite a few fixes for that problem. I took all the trim off on my blue wagon, peeled off the plastic and then sanded. I then painted a basecoat of light brown and then spotted it with a dark brown. It came out real good. I think I did it 5 years ago.
Some other guys, remove and then buff it, to it's stainless color.
I think if I were you, being in Norway, I would do it on the car. The reason, if one of the clips breaks, it's a little bit of a problem getting the replacement in Norway.
The wood trim is aluminum, and therefore can be polished. If you tape the car about 6 inches on both sides, you should be able to remove the finish or polish without harming the paint and woodie sides.