> it would be awkward for any country to have to hand over its elected leader,

Since the leader (elected or not) generally controls the executive apparatus (that’s what makes them the “leader”), its unlikely that this would actually occur, irrespective of the nominal obligation. It is more likely that they would be turned over after being removed as leader (a process which an ICC warrant may or may not accelerate, depending on the response of other institutions, the populace, etc.)

At least, that is what has generally happened with the top leaders that have ended up at the ICC (or its predecessor ad hoc tribunals, back to Slobodan Milosevic, the first sitting head of state to be charged with war crimes by an international tribunal—the ICTY—who wasn't turned over by Yugoslav authorities until after he resigned.)

> because Europeans disagreed with a military decision

The majority of State Parties to the Rome Statute are non-European, as are a majority of the current judges of the court, as is the current acting chief prosecutor, so it is really weird to describe ICC involvement this way.