That looks right, but I'd just get a CR2032 holder and be able to swap batteries in the future.
Here is an example that would be easy to attach. I plan on doing something smaller/lower profile,
like this, but that's going to be slightly trickier to attach.
As for my 'prettier replacement shell', I've realized I'm really butting up against the size limits of what I can reasonably CNC, especially with final wood thickness and the metal details (I was thinking polished brass would be a good 'Swedish gold' stand-in). I have one design that might work, and I'm tinkering with the idea of 3D printing a core and then wrapping that with an Ash veneer in order to save some thickness.