A paper wallet should be always offline. Otherwise, you would defeat the purpose of a paper wallet.
Since you can only sweep your private key into an online wallet and there is no way to sweep a private key into an offline wallet, it's better to import your private key into an airgapped device and sign the transaction offline.

This is assuming you have created your paper wallet on an airgapped device in the correct way. If you didn't do so, you have already defeated the purpose of a paper wallet and your paper wallet isn't really a paper wallet.