Visiting Mykonos on charter is sometimes a possibility, however the winds around Mykonos are usually very high (the islands nickname is “The Island of the Winds” because of the very strong winds that usually blow on the island) making it difficult to sail into. You can certainly discuss the option of visiting Mykonos with your captain when you arrive. He’ll have a better idea of the weather forecast.
We recommend a charter with us to visit the authentic and less touristy Greek islands and then booking a stay for a few nights in Mykonos before or after your charter. The flights from Athens are very inexpensive (around €50 one way) and quick (40min) or you can also take a 2.5hr high speed ferry.