Suggestion for Airgap Bitcoin Core - Comments?
If I understand you correctly, Im not sure your system will work, because your air-gapped laptop is never connected to the internet, the transaction wont get broadcast.  You can try it, I may be wrong.

I have done a similar process using rawtransactions, where you prepare the rawtransaction on an online computer, using an explorer API (https://chainz.cryptoid.info/api.dws is one that I found works) you get the tx input and vin, create the rawtransaction and save the hex output to a small USB (smaller the better).  Then on your airgapped machine use signrawtransaction to sign it, then transfer that hex output back to the online machine and sendrawtransaction.

I automated that process in Python, you can see how it works in more detail on my github https://github.com/Scalextrix/coinofflinewallet

It worked with QR codes as well for a fully airgapped solution, but I had a lot of trouble with the Python webcam/QRcode libraries and ended up not bothering.  My code is not extensively tested, its really an example, you should validate it fully before use.