Ah, I may have missed it in this thread, but I don't recall what features of Calibre the poster wants to support.
I.E: If collections management, then Calibre will need both access to the user store and a way to remotely do data base updates to the collections data base.
If the "wireless" request is only to avoid a bad USB connector -
The poster needs to solve how they are going to keep the battery charged first.
(famous last words here): It shouldn't be too hard to float off a good connector with hot air from an otherwise junk Kindle and use it as a replacement for the bad connector on the otherwise good Kindle.
Our dead horse may still have one leg twitching - if we could get a few more details of the end goal(s) of this inquiry.