If all else fails, you could suggest that you leave it at the check-in desk on the way out. Cinderella could then "pick it up later".
I just did this for my 5-yr-old who wanted to give something to Tigger at a character meal. Of course, Tigger has no pockets and, to make matters worse, can't talk. When I suggested leaving it at the front desk, Tigger shook his head excitedly and gave her a big hug. It was very cute to see how serious she was when we stopped at the front desk and she explained that she was leaving something for Tigger. The CM played along and said he would make sure Tigger got it. My daughter was very excited and talked about it all day.
As the previous poster mentioned, the characters often have a handler that might serve this role. But I think this is just when they're out in the parks. When the characters go around at a meal, I don't think they usually have a handler with them.
At least Cinderella can talk, so it should be much easier to work something out.