Dd2 was diagnosed at the twenty week scan as missing her left arm from below the elbow, so I do understand what you're going through.
When the row about Cerrie Burnell kicked off in the media, I was very concerned that it would effect dd2 because so many nasty things were being said about her. Actually within a couple of weeks it became very clear what a positive thing it was. Not only was there someone on CBeeBies who dd2's friends could relate to, it actually meant when out children were coming up wanting to be friends because dd2 was "like Cerrie".
For other children to see people with your child's disability on TV being treated as a "normal person" it helps them to treat your child as a "normal person".
Warwick Davis, from interviews with him I've heard, will very much treat your child and others like him with dignity and respect, but it is very normal to worry about it.
In the first few months I couldn't have seen the funny side of dd2's condition. However now I (and she can too) can chuckle at some of the situations it's got us into. Like the time an old lady raced after us shouting "your baby's broken her arm" when she'd got her prosthesis on backwards. When people are unsure how to treat dd2 often telling a few things that make them laugh can help them to relax round her and then she just becomes one of them.
Have you got contact with other people with the same condition? Do they feel the same way?
If they do, then I'd suggest you approach the BBC as a group and ask if you can view it ahead of its release. That way maybe you can discuss with them anything you find offensive. I think that is a more reasonable approach than just asking for it to be banned, and more likely to be taken accound of, particularly if you're doing it under a known group.
HTH.