download last Electrum version verify signature and add your private key/wallet seed.
Correction: paper wallets are almost always only made with private keys, using a seed phrase when you create a paper wallet is especially uncommon so it doesn't even need to be mentioned.
There is no reason for you to broadcast that Old transaction even though broadcasting it will not pose a risk as you have the private key for both addresses.
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Sign a new message and then broadcast it.
Why though? The point of having a signed transaction stored away is so that you can safely broadcast it in case of an emergency.
For example an armed robber breaking into your house where you'd have enough time to broadcast that signed transaction (assuming you have wallet software handy and the tx was stored electronically!) but you would not have enough time to download Electrum, verify it, import your private key, fill in a receiving address that you have to recall from your head or notes, then then enter a password you made up to sign the transaction because you wouldn't put your cold storage at risk by not password-protecting a temporary wallet (right?) and finally broadcast the transaction before he comes to you and interrupts this demands at gunpoint that you send it all to him.
Each time you load a private key, especially for a paper wallet, into wallet software, you are exposing it to risk even if that amount of risk is small. When it holds very large sums of bitcoin it is better not to do it unnecessarily.