I now want to sweep Bitcoin from a paper wallet to Electum. Which wallet do I have to use for this?
Is your paper wallet encrypted? If the answer is yes, you can decrypt it using bitaddress.org before using any wallet to send into Electrum. None of the wallet, I know of supports BIP38 decryption.
And if the answer is cold storage: Does the computer have to be online for this?
Honestly, its up to you if you want to sweep into the offline wallet or the online wallet. It's totally dependent on your own preference; online wallets are more suitable if you want convenience and offline wallets are much less convenience.
Anyways, you don't necessarily need your computer to be online for this. Just the creation of unsigned transaction and the broadcasting of transactions.
Oh.. Your question isn't crystal clear. If you're saying whether you should use the online or offline instance to send coins, you can import the address into your online wallet, get the raw unsigned transaction, import the private address into your offline wallet, sign it and broadcast it on your online wallet.
