On the topic of wood for our cars, keep in mind the following:
1) There are several aftermarket suppliers, so check around if you are into replacement. I believe that some of these reproductions are solid mahogany or similar as opposed to veneer.
2) The original wood was an extremely thin veneer, so thin that it didn't take well to much sanding in a refinishing process.
3) There are several refinishers of Mercedes wood that advertise in the Star and in other publications. They make a specialty in automotive wood refinishing and I believe they come with excellent references. Heritage Woodworks is one that comes to mind immediately.
If you opt to do it "locally", there are generally many fine furniture refinishers that can handle the project. Make some phone calls and the good ones will rise to the top of your list quickly. I had mine done locally years ago, and while not up to "new" quality or that of Heritage, the work done was quite nice and a fraction of the cost of "Mercedes" refinishers--perfect if you are on a budget.
If you live in a large metropolitan area, and want to have it done, seek out a piano rebuilder. What you say? A Piano rebuilder? Yes--the folks that rebuild pianos have unparalleled skill in the fine art of finishing and refinishing, with all kinds of veneers, finishes, toned varnish (that's what Alan H refers to) etc. Many work on furniture and fine wood too, if the piano business is slow. I've seen what amounts to firewood restored to original glory in a piano restoration facility, so it's worth a shot.