I have a 9"x14" carving of a sailing ship that was once part of a coffee table. It's about 50 years old. It's carved in an oval on a 1" piece of some sort of close-grained wood. It has a really dark stain that appears to be covered with some sort of varnish.

There are a lot of small spaces that I don't think I could sand.I'm having trouble getting the dirt out of them! Any ideas about how to remove the finish without ruining the piece?