Several points:
(1) Check for "Apple Authorized Service Providers" somewhere near you. They can be found on Apple's web site under Service. Some of these independent shops will actually do the work in their shop (you can simply wait there for them to do it). Some will send it out, however, so check on that if you find one.
(2) I think there are three factors for you to consider:
- Is your current watch working well and meeting your needs?
- Do the newer watch models have features that you very much want to have?
- Is the cost worth it in light of your answers to the two questions above?
My bias is as follows: with Macs, iPhones, printers, routers .. we tend to keep these things as long as they are working well and are healthy. A new battery is not a major service item. I have a 2013 MacBook Air that was "revived" several years ago with a new battery. My wife's iPhone got a new battery several years ago. Both of these services were performed in less than one hour while I waited in person. So if you really like your current watch ... I would get the battery replaced. Unless money is not a constraint, in which case, why not get a newer model with new features and ... by the way ... the newer watches often have much better battery life and longevity.