Hi Ragdoll, I had the same problem where the cord was fraying, so I went to the Apple store in Jax. Fl and they just gave me a new one without hesitation. I hope you are near an Apple store where you can do the same.
I didn't have such luck with an easy exchange when I had the same issue. So annoying! My friend actually told me about this stuff called SuGru. It's a 'new self-setting rubber for fixing, modifying and improving your stuff.' Really handy stuff & has excellent reviews of what its capable of.
You'll only need a little bit for this iPad cable fix; just an alternative if you can't get a replacement easily.