Edit: The new owner of my account has messaged me and is stating that he is not the hacker but bought it "the telegram" and wishes to return my account for what he bought it for, 0.08 BTC.
I believe your private key can be imported into Bitcoin Core under the console which appears under the Help / Debug menu. https://en.bitcoin.it/wiki/Help:How_to_import_private_keys_in_Bitcoin_Core_0.7%2B
There are other ways to import the key into a wallet but I'm not sure I would trust most of them. Does your paper wallet contain an encrypted private key?
IMO, if you have any chance of verifying the account with a signature, I wouldn't pay anything to whoever PM'd you.
How are you intending to sweep the address without getting the paper wallet imported? I'm confused