I def prefer to install new on the airgapped Win10 rather than try to upgrade and mess with the old Win7.
I agree... stick with Win10. I wouldn't even bother attempting to do anything with the old Windows 7 Laptop. It's only really going to cause more issues
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?
Correct. You just use "Standard Wallet -> I already have a seed" during the wallet creation process. Then input your 12 word seed and Bob is your mother's brother! NOTE: you won't see any transaction history (as the wallet is "offline"), but you will be able to see the addresses and confirm they're the same.
So, download and verify Electrum from:
https://electrum.org/#download You can follow abdussamad's very useful guide on how to verify your Electrum download using Windows here:
https://bitcoinelectrum.com/how-to-verify-your-electrum-download/Once you have it installed on the airgapped machine, and the wallet restored using your 12 word seed, you can just goto "Wallet -> Info" and get your "Master Public Key" (aka XPUB) from the window there and then use that xpub on the online Win10 machine to create the "watching-only" wallet (Standard Wallet -> "Use a Master Key" option during wallet setup)
Then you'll be able to see the full wallet history on the
online machine... and you can create a transaction (click "Export -> to File" when prompted) and save the ".psbt" (partially signed bitcoin transaction) file... copy the .psbt file to USB to transfer to the "offline" machine, open the .psbt file on the "offline" machine using "Tools -> Load Transaction -> From File"...
Then sign it... "export -> To file" and this time it will be saving a ".txn" (completed transaction) file... copy that .txn to USB, transfer back to "online" machine... open in Electrum using (Tools -> Load Transaction -> From File)... double check everything looks good and "Broadcast"!