If Cyprus was part of the Ottoman Empire after WWI, when the "population exchanges" occured, would Cyprus have been considered Greek (or to be more exact "Christian") or Turkish (Muslim)?
Turkey was the only country to negotiate its treaty with the Allies, so it may have seen how much it could get away with... My view would be that Ataturk would have strived to make it Turkish, as I'm sure he was quoted to have said "the turn of Cyprus is yet to come". Great Britain certainly didn't want another war on its hands at the time.