Reporting back, did some research on removing cig. smoke and tar from houses, someone suggested plain shaving cream
I guess there's a chemical in that which kills the smell and breaks down the tar.
I took the whole watch apart, removed the movement, scrubbed down the band and case in shaving cream, and to my surprise it seemed to be much better in smell and look. Then I cleaned that and treated it with a "enzyme cleaner spot treatment" (like Shout it Out in the States).
Once that was complete, I used some sneaker white polymer to clean up the band and case.
I'm now pleased with the results, the smell is gone and it's minty two shades of white.
Thought I would pass it along to future generations