Mykonos Disembarkation (early)/Immigration

[hkdad3]

I will leave my cruise one day early in Mykonos, and I have obtained permission from Princess for this already.  I have a flight within a few hours of the ship's arrival in Mykonos, departing from Mykonos airport.  Does anyone know what the immigration process will be?  I am a US citizen, and the cruise itinerary is from Rome to Athens.  Both Italy and Greece are Schengen countries of course, although there is a stop in Montenegro (non-Schengen) along the way.  Is it possible there will be no immigration formalities for me in Mykonos?  Would it make a difference if I don't get off the ship in Montenegro?  If not, will the process in Mykonos be quick?  Would it be possible to clear immigration in Crete (Chania) the day before (or Corfu the day before that)?  Any advice would be extremely helpful.