So I am guessing that electrum provides you with something like a QR code and you use your device to read it and sign it. Like the seedsigner device, which I absolutely love. Correct ?
Correct. You would create what is called a watch only wallet on your online computer, which contains only your addresses but no private keys. This wallet can be used to watch your addresses, balances, transactions, etc., but cannot be used to actually sign any transaction or send any coins, since it contains no private keys. You use this watch only wallet to create an unsigned transaction, and then either display that unsigned transaction as a QR code on the screen, or export it to a text file. Then with your airgapped computer with your cold Electrum wallet, you either scan this QR code or transfer over the text file using a USB drive or similar, and use your cold wallet to sign the unsigned transaction. Then reverse the process to move the signed transaction back to your online computer and broadcast it to the network.
So, speaking of paper wallets, how did you generate them? The whole point of this thread and the fact that I tried to develop something is that I didn't trust bitaddress for example.
If you want an classical single key paper wallet, then I would simply use Core on an airgapped computer to generate a private key and then copy the private key and address to a piece of paper to be printed with a dumb printer. I prefer to use seed phrases to generate HD wallets, though, rather than individual key pairs. For this I would either use Electrum, or generate the seed phrase manually by flipping a coin. Write that seed phrase down, and then use Electrum to derive the relevant addresses from that seed phrase to either also be written down/printed off, or transferred over to an online machine via QR code. Once you have the seed phrase written down and some addresses to send coins to (and double checked everything!), you can wipe all traces from your airgapped computer.