Other ways of dealing with McCluskey?

Considering he was a direct eyewitness to Michael assassinating Solozzo, yes, Michael had to kill him. A few shell-shocked innocent bystanders is one thing, but McCluskey is both a NY Police Captain and a hired goon in the pocket of the Barzini family. Leaving him alive would mean a death sentence for Mike, either in the prison he is locked up in, or eventually in Sicily when more of Barzini's thugs come for him.

michael-judd is right: Mccluskey HAD to be killed. The Corleones had to have him dead, to protect Vito, and the Barzinis had to have him dead, for failing to get Vito assassinated.

Once he was involved, there was no safe way out, for him.

- Lord, have mercy on a country boy

Killing him was the 'masterstroke', with McCluskey, Sollozo thought he was untouchable, and McCluskey thought HE was untouchable, even the cruelest thug wouldn't dare to kill them, let alone a civilian who let himself being slapped in the face, Michael went against the odds and knew it was the right thing to do and it worked, because it was the only was it could work. There was no political influence to use, the Don was sick and it's to preventing from further murder attempts that the Turk and McCluskey had to be killed asap.

Darth Vader is scary and I  The Godfather

You know, it really didn't occur to me until I read this post, but this was the way the Corleone Family should have dealt with McCluskey: rather than have Mike shoot both McClusky and the Turk, they should have used their contacts and influence in the press to publish information regarding McClusky's affiliation with Solluzo. Once the news about McClusky being mixed up with the rackets was reported, he would have had no other choice but to resign from the NYPD. This would have made the Turk "vulnerable," in contrast to how Hagan characterized him, and would have enabled Sonny to go with his original plan to have the Turk knocked off. Of course in the movie Michael's plan was to kill McClusky first, then have the newspapers release stories about his mob involvement. Maybe Sonny was right--Mike was taking the fractured jaw "very personal."

But that would not be justice.