Well, you can skip the mobile phone and it will be even faster.
1) Create unsigned transaction on your online PC and display the QR
2) Scan the QR code with your offline computer
3) Sign the transaction and display the QR
4) Scan the QR code with your online computer
5) Broadcast the transaction
But you could also (if you don't have webcams or don't want to use them) do this:
1) Create unsigned tx on your online PC and display the QR
2) Make a photo of the QR code with your mobile phone
3) Move the photo onto your offline PC
4) Use a QR code reader software on your offline PC to decode the data
5) Import the unsigned TX into electrum
6) Sign the transaction and display the QR
7) Do 2) - 5) with the signed tx from your offline pc -> online pc
8] Broadcast the TX
The second approach is more time consuming and requires a software to extract data from QR codes installed on your online AND offline PC.
I, personally, would choose the first option for dedicated offline storage.
Bob123, thank you very much for your interesting ideas!
You are right , I don't want to use my notebook's camera to scan QR codes from my PC. My PC screen is actually my smart TV hanging on the wall, it I would be extremely uncomfortable for me to scan anything from that screen with the Notebook.
So , I should use either your method 2 or my own method (copy-paste described above) . Both methods are complex and inconvenient