I'm thinking a china vs. india epic dance battle would be a good way to address the border issue.
For cyprus, the greeks and turks could just speed up the music until some team loses the beat. Spratly islands could be sorted with synchronised swimming?
I mean, this is kinda what the olympics does, right? Show off how good you are at making soldier-like people, celebrate some nationalism, acknowledge that the other countries are also humans capable of training good soldier-like people, and then everyone goes home and continues trading.