I don't know about a watch but a power supply using kinetic energy would work such as a small lever that you could move. Kinetic power supplies sound nice but they are usually way more expensive that a battery even after you factor in the life time battery costs associated with powering the gadget. Plus it's inconvenient. It's way more practical to have a general purpose kinetic energy power source.

Here's an article that will give you some insight.

https://en.wikipedia.org/wiki/Energy_harvesting#Human_power