You need to use an offline computer, preferably a permanently airgapped one with a clean OS, import your private key there and sign a transaction on this airgapped computer, and then move the transaction to an online computer to be broadcast. There's a good post from LoyceV about this here, which I'll just link to rather than re-hashing all the information - https://bitcointalksearch.org/topic/m.56389821. Make sure to verify your Linux and Electrum downloads before installing/using them.
Your are bang on correct. It's a very old paper wallet and I am not able to import it into any new hardware wallet. But I want to learn the most secure way to move said paper wallet into a Ledger.