Welcome to Cruise Chat The Hathaways.
I have always said, I'm on vacation, and do not ever want to wear a suit and tie-however, I've seen men in a tux, suit and tie, and sport coat and tie. I wear a pull over golf shirt and slacks, and have never had a problem or been told that I was not dressed as I should be dressed. We've even had photos taken on formal nights with the nice back drops provided.
The on-board cleaner does a wonderful job-I don't know how delicate you're talking about, but I'd say that they are on a par with your regular dry cleaner at home. Men's shirts that I've had cleaned come back on a hanger, not folded and boxed as some on shore cleaners.
Checking your bags on the plane? Depends on the bag size as to if they'll allow it in the cabin.
On the ship, to get on, you will have to use a ship's porter. Getting off the ship, you may use the option of carrying it off yourselves. I would imagine that would make it a little slower getting through customs.
Which ever you do, have a great cruise-you're going to love it.