Hi Tom & Mary,
While I'm sure this is fun for you, from what I've heard on message boards and from our stewards, $2.00 bills are not really good for tipping. The "tipee's" have to take them to the Purser's office to get them changed into "real" money. Many overseas banks won't accept $2.00 bills. They are also leery of the "new" $20's. It's best to tip in smaller bills or with old $20's.
As lougee said (sort of!), the staff will go along with whatever you do. Unless you ask, they're not going to say that they don't want these bills. I also agree that it sounds like you're talking to a child. JMO.