Judahis,
Yes, you need an Internet connection to register Kindle for PC, but once you've registered it, you can use it to read Kindle books without an Internet connection.
The same is true of the Kindle itself. You can either register it directly from the device, or you can go to the Manage My Kindle page to register it from your PC. Either way, you don't need any kind of connection to actually read the books.
In your case, you can transfer your existing books to your Kindle via USB. Assuming the Kindle and your copy of Kindle for PC are both registered to you, you can then start reading - with or without an Internet or Whispernet connection. Similarly, if your second copy of Kindle for PC is registered to you (or, to be precise, the same user as the first copy), you can transfer your books via USB and read them on both computers.
The only thing you can't do without a wireless or Internet connection is to sync the last page read.
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