As I see it, it's pretty simple.
If you're basing a work on the original novel and printing it in the United States, you're golden. Nothing in the US older than 1923 is still under copyright, all of it having become part of the public domain.
If, however, any part of that work can be confused with or identified as being from a still-copyrighted derivative work, like the aforementioned movies and TV show, and it is not a parody of said derivative work, that's where the trouble begins. The depiction of Captain Hook in the deck, for example, bears a striking resemblance to that of the movies "Peter Pan" and "Hook", both of which are very much still under copyright in the United States and property of the Disney Company.
As far as needing USPC permission to claim a project will be printed with them, well - I've seen countless projects make that statement. Without a signed contract in place, it's a little harder for them to dictate such terms. After all, we say "deck designer", they say "potential customer", so they're not going to push too hard on the subject, unless the designer has no intent of printing with them at all. USPC will help with a little bit of the planning work needed before a KS launch in terms of supplying best practices documents and templates and such, but as was previously stated, they don't begin actually vetting a project until a contract is signed and funding is in place. It's not impossible that they'd reject a project for certain reasons, but I've never seen them go that far - the closest would be a non-KS project, the Karnival Inferno deck; the company forced a redesign of the artwork to remove some of what they perceived as the more "Satanic" elements and the Bicycle brand name was removed.
Without making modifications to the art or obtaining a license from Disney, he stands a good chance of running into legal problems.
And absolutely none of this takes into account trademark law - with proper renewal and lack of dilution, a trademark can be renewed in perpetuity. It would surprise the hell out of me if Disney didn't take some effort to trademark their depictions of the characters from their version of "Peter Pan" and any derivative works they've created.
Trademark law, not copyright law, is what USPC uses to keep others from printing Bicycle Rider Backs, claiming a trademark on their unique card back design as well as the jokers and the Ace of Spades. The rest of the deck's design can't be defended under any such law, because there's hundreds of years of prior art - it would be like claiming a trademark or copyright on the alphabet or the Declaration of Independence.