I will boot from USB and try Ubuntu.
Insert 8 GB USB install Electrum.
Extracting the public key.
Sign the transaction.
Broadcast the transaction.
Remove Boot flash and back to normal parts.
I think that you either wrote it wrong, either I'm understanding it wrong.
The "cold storage" Electrum should never go online, still you seem to broadcast tx from it.
So if possible, I'd put Electrum onto the Ubuntu stick too and keep the smaller stick for transport (if that's not possible, consider a 3rd stick for transport).
After the offline Electrum is running, copy onto the transport stick the Master Public Key and shut down Ubuntu.
On your usual OS you make a watch only wallet from that Master Public Key, that's where you create transactions, that are exported to the transport stick.
Ubuntu is loaded up again, tx is loaded from transport, signed and saved back to transport and Ubuntu down again.
On your usual OS you load from transport the signed tx and broadcast it.
I wrote as the "airgapped pc" is the same as the normal pc and you switch between them. If there are 2 different physical PCs it is much easier.