Lost and found on Cycladic islands

On a hike yesterday my girlfriend and I found a watch that could have considerable value to someone on one of the smaller Cycladic islands in Greece. We've been asking around whether somebody reported it as lost. At the police station we've been told reluctantly that they would keep it until the owner claims it or a year passes. We are not convinced this would help, because they seem to lack any kind of lost & found infrastructure. Does somebody know of any alternatives?