Rechargeable watch?

I'm not sure if there are any rechargeable watch around. Well, I am in a tropical island... very laid back. Not so tech-savvy.

I went for a hike a few weeks ago. And my watch went dead. Or should I say out of charge? It there any expression in English when one need to replace the battery. I'm not a native speaker, please excuse my English. (Over here if anything needs its battery replaced, we would say that it died... maybe because we are so emphatic towards our gadgets and electronic goods)

I still haven't replace the battery. Because now I rely on my phone clock. Even the clock on the dashboard is not showing the right time. It is 10 hours 40 minutes late or maybe 13 hours 20 minutes earlier. So it would be very useful in the middle of the Atlantic... So when the dashboard showed 2350, it's really 1030.

I had the car battery replaced after a big flood fried the ECU and never change the time on the clock. So anybody driving the car would think that it's some sort of gauge instead of a clock.

Back to rechargeable watch. If only I could just recharge the watch instead of looking for a watch shop to replace the dead battery. The watch in question is a Casio, it has both analog and digital display. There's no physical seconds hand (or needle, we called the hands on the clock needles) but it has a 'digitalised' seconds ticker. With the added features (like most Casios) it uses  button batteries instead of one.

The last time I replaced the battery was 4 years ago, because the digital display began to look fuzzy... or faint? And I would need the watch to count the pulse rate and other vital signs. I was still in the big-city then. I bought the watch at a town-near-a-big-river 8 years ago. It's still in a good shape.

I like the watch, It has been with me since before I have PTSD.

p/s I am aware that there's such thing as smartwatch,