Actually I may have to eat my words about Ubuntu.  I just found this minimal install ISO.

https://help.ubuntu.com/community/Installation/MinimalCD

It's a netinstall so the computer will have to be online to grab the packages but I don't see that as a huge issue.  IIRC Ubuntu by default verifies all the packages it installs via GPG signatures.  The plan is to grab all the packages that Armory needs while online then disconnect, blacklist the wifi module, and never connect to the internet again.  Then only after I'm offline for good will I install Armory and generate my private keys.  Updates don't really matter unless it's something that directly effects Armory so I won't even both with those (if it is something that affects Armory I'll just grab the .deb from my online computer, verify it, then copy it over via USB driver... same with updates to Armory itself.)

The downside is they state it doesn't work for UEFI boot.  My UEFI-based desktop supports BIOS emulation (which is actually the default mode) so this isn't an issue there but that's my main online machine.  I have a laptop that shipped with Windows 8 I would like to use as my offline machine so I don't know if I can BIOS boot with that or not.  We'll see in a little bit I guess.  For now, I'm just testing it out in a VM.  Here's a screenshot of the most bare-bones Ubuntu install possible:

http://i.imgur.com/1rRyIPV.png