Solved it. The UI has definitely changed quite a bit and the documentation on electrum.org is out of date.

I needed to click 'Pay ...' on the 'Send' tab, then 'Send' on the dialog that appears after that, then there's a second dialog that allows the export via QR code, etc.

Thanks again for the help, everyone.

Hey, thanks again HCP and NeuroticFish. I've completed the (verified .exe) install on the airgapped Win10 machine via restore seed and the setup of the watching wallet on the online machine. I see the transaction history on the online machine, so all good there.

But I'm not seeing the option to export an unsigned transaction from my watching wallet:

I'm on the 'Send' tab and have entered the destination address and the amount, but the only options I'm seeing are 'Clear', 'Save', and 'Pay...'. Clicking 'Save' just creates an item in the 'Outgoing payments' table below that with status=Unpaid, but I've gone through all the contextual menu options and cannot find an 'Export' function.

The UI also doesn't match the cold storage documentation, so maybe some things have changed for 4.0.9? There's definitely no 'Preview' control on the 'Send' tab as indicated here:
https://electrum.readthedocs.io/en/latest/coldstorage.html

I've double-checked the signature verification of the install file, which I got directly from electrum.org. Any ideas?

Thanks so much for the fast replies. I assumed jackg meant download and verify Electrum on the online PC then transfer to airgapped via USB, as you said. 100% with you.

I def prefer to install new on the airgapped Win10 rather than try to upgrade and mess with the old Win7.

So if I'm installing on the airgapped Win10 machine, do I go through the restore-using-seed process to essentially replicate the Win7 wallet on that machine? Or something different? Wasn't sure if that'd work while airgapped. If that seed-restore works and is safe on the airgapped Win10, then I think I do understand the process for creating the watching-only wallet on the online PC and using that to initiate the transfer of any coins into a hardware wallet.

Thanks in advance for any help. I've dug through the archives and Electrum's documentation but I'll admit to being very confused about my best path forward.

Goal:
Transfer access of BTC and any worthwhile forked coins (BCH, BTG) from an offline version of Electrum 2.6.4 to the newest version and/or a hardware wallet

Situation:

• Last accessed my Electrum wallet in ~2016. It's v2.6.4 on a Windows 7 laptop that has been offline since then, and that I will not be connecting to the internet again. I'm aware of the security vulnerabilities in running that old version while online. The laptop runs and I can still access Electrum on it via password. I know my 12-word seed.
• I also have a new airgapped laptop running Windows 10 that has never been online, and another PC running Windows 10 that is online all the time. I'm not well-versed in Linux -- all Windows machines here.

Key questions:

• I could install the latest version of Electrum on the online PC and restore my old wallet using its seed, but I'm reluctant to type the seed into an online computer. What would be the most secure way to move any coins from the addresses I control, either to the latest version of Electrum or to a Trezor or Ledger? I'm not clear on whether there's a way to, for example, do a restore or sweep using an exported wallet backup from the 2.6.4 version with my password but not the seed.
• Is it possible to install Electrum new on the airgapped PC and then restore the old wallet via seed, while never going online? And then issue a signed transaction that I could copy over to the online PC for broadcasting? Or does Electrum need to be online to restore a wallet from seed?
• Alternatively, I believe I can get the Master Public Key from my Electrum 2.6.4 wallet. If so, what if I create a watching wallet on my online PC, then create an unsigned transaction on the online PC -- would there then be risk in moving that to the old offline PC still running Electrum 2.6.4 and trying to sign the transaction on that old version, then transferring back for broadcasting? I'm not even sure if that's possible, let alone sensible.

I'll be very grateful to anyone who might help lead me down the right path here. Any pointers on the best way to deal with BCH and BTG after dealing with the BTC would also be welcome. Thank you so much.