you could write a little script that does this, it would be a good way to learn that stuff. Once you've updated the online machine's Bitcoin-qt 5+ times, the novelty of how cool gpg and sha256sum are will have worn off, you can return to simplicity with the comfort/satisfaction that you know alot about what's going on when your software is being checked for authenticity. And you also get to debug the script when one of your assumptions turns out to be bad, hurrah!!

none if this ever mattered to me back in the Windows days, I figured that either software worked or it didn't! But once I was in solely in charge of keeping my own money safe, my attitude quickly changed