Adapting to whatever battery exists 200 years from now to the form of a CR2032 battery would be simple. A Casio just takes a round battery shell that contacts with the positive and negative terminals on each side.
Hell, I can make one from scratch in my workshop trivially, from basic materials.
Finding high-end mechanical watch technicians? Not so easy. And hardly so cheap.
The Casio would last even longer - and would be closer to the right time even without touching it in between.