I found a perl script a few years ago online that would take a GPX file and a folder of images, and geotag them using the timestamps. I recall it working pretty well. I think it was https://jmorano.moretrix.com/2011/04/geotag-your-photos-with-perl-and-gpx-files/.
That simplifies that, but let me add another wrinkle. There is a distribution of android for raspberry pi, a pi zero and a BLE module could in theory be installed with android. In that case, would the android SDK be enough to connect to a watch over BLE? I could push location data out to this android device at that point right? From there I could push the location to the camera via a wired connection.
If all of this seems crazy, I'm looking for a low cost solution to use the watch as a GPS instead of one built into the camera or one on a phone, because both are notoriously bad for battery life.