Sounds perfectly suited for watch batteries.

I prefer changing the battery once every three years over having a radioactive emitter strapped to my wrist. There is a decent case for nuclear pacemakers since changing the battery of those requires surgery, and even there it didn't get traction. Watch batteries are quick to change, I don't see the risk/benefit tradeoff working.

And with smart watches we are back in "useless for most applications" territory.

My wristwatch's "face" is a solar panel - Citizen Eco-Drive. Had it for around 20 years and it has never stopped.

Nah, too bulky and there are already better solutions. If you have just a classic watch, then a kinetic charging mechanism is something that's been around for ~100 years. Your watch auto-charges from simply wearing it and walking around.

But if you need more juice, then solar watches are also a thing that work pretty well.

For a smartwatch, these batteries won't produce enough power to keep them going. It's better to just slap a bigger battery into the watch rather than a nuclear battery + regular battery.

Until they reach the dump...

Watches tend to be exposed to light a fair bit, so putting a solar panel in the watchface easily outperforms a betavoltaic cell. This has been available for decades, and even some of the high-end Garmins have it.