Yesterday, I had to get some watch batteries replaced and some watch bands sized. The place, that is the best and most reasonably priced shop that I have found, is El Marquez Watch Repair. it is located at the corner across from Banco General downtown. They have opened another shop down the same street on the other side of the Casino. The second shop is close to Parque Cervantes.
This is a photo facing the Bank to help orient you.
The gent you see here, is usually in the shop. He does good work and is fast when it comes to just a battery replacement or size change.
They also service and repair wall clocks.
If you stop in, tell them that you were refereed there by Chiriquí Chatter.