My niece has been deathly afraid of anyone in a costume since birth - Santa, Easter Bunny, Clowns, The Looney Toons characters at the local six flags etc. She would not even stand 10 feet away. I was always her protector, she'd see a character and she'd jump into my arms and hold on as tight as she could. She would be physically shaking. It was really bad.
We were doing a big family cruise on
DCL when she was six and still deathly afraid. She would be with her sister and three cousins, all ages 3 to 6, but that never seemed to matter, she saw someone in a costume and she freaked.
Unfortunately I can't give you advice on the cruise. We were all very worried. We were doing four days at WDW before the cruise and her aunt decided to book the entire family a Character Breakfast the first morning. Great way to start the vacation.
We were outside of AK waiting to get in when she had a total melt down realizing that there would be characters inside. She dropped to the ground just screaming. Her mother took her aside and assured her that she wouldn't have to go near them and that we would all 'protect' her. She entered the park sobbing but went along with the family.
At the character breakfast we tipped off the staff of her phobia. The indicated that they see that a lot. (I would assume that the same would be true on the ship). We had a large group so we sat at two tables - one was the character table the other was the NO character table, the cast members let the characters know not to go near the table. They did wave but even that upset her. She was hiding under the table sobbing. After a few minutes she started to peer out and saw all the other kids having a good time. Eventually she climbed out on Grandpa's lap and waved to Goofy.
She calmed down and we made it through breakfast. As we were leaving we walked by a character greeting area where Winnie the Pooh was standing. There wasn't much of a crowd and we had not intended to stop. Suddenly my niece broke away from the group and ran towards Pooh and gave him a huge hug. We were all flabergasted (as was Pooh I'm sure). From that moment on you couldn't get her away from the characters. We bought her an autograph book and was was fixated on getting as many autographs as she could. She could have cared less about the rides and shows, she wanted to see the characters.
So by the time we got onboard the Magic her phobia was long gone.