If you've downloaded the update... checked the digital signature (in the case of Electrum)... And transfer it to the air gapped computer, do you think that a user would be running any more risk than copying your transactions back and forth via USB?

Even if you messed up and downloaded a compromised version of the wallet... the fact that the computer itself is air gapped, should prevent any wallet/key leakage. At worst, the malware would only be able to try and slip something out via your USB... or potentially tamper with the transaction in some way (ie. change destination address during signing)

I would have thought that doing you due diligence of double checking your transactions and/or USB for anything "odd" should help prevent that.