All of my internet is wired (using home plugs) so I've had my Kindle in aeroplane mode since purchase. The kindle (paperwhite) itself remains unregistered, but I had a telephone conversation with an Amazon person soon after purchase. They registered the kindle at their end so that I can buy and download books for it (transferred via usb) and they explained how to do the transfer. I didn't need to have the kindle itself registered at my end.
Certain functions don't work if you're in non wifi mode: the vocabulary builder, x-ray, wikipedia search, translation, collections, synch. The dictionary and search still work and all other BASIC functions. Naturally, it can't connect to the internet in any way.
I suggest that you contact Amazon. I doubt that you need to de-register your kindle, just make sure that when you download a book from Amazon you choose the 'transfer via usb' option in the drop down bar (on the book's Amazon page), then when it asks which device you want it for (during the purchase process) pick the name of your kindle. A message box will appear asking you to save the book, press ok, then it'll download onto your computer (all my downloads go to the desktop).
For a mobi etc book, you don't really need Calibre, unless you create Collections there. Just stick the usb lead into your kindle and computer, go to 'my computer' find 'kindle' then open this. Open the 'documents' you'll see in the kindle box, then slide the book into there. Close down the kindle box (click X), then eject the kindle from your pc. Leave the usb attached if you need to charge your ereader, or just pull it out if you're finished.
Here endeth the lesson!
