Mmm I'm pretty sure you can:
1. run Armory without internet connection
2. Create a raw transaction, moving the funds
3. Sign the raw transaction
4. Close down armory, and with good old bitcoind you can use the (command line) "sendrawtransaction" command.
Be careful when creating the raw transaction though. Without an internet connection you'll have to check the validity of the raw transaction. Armory won't be able to.
You can't create transactions in offline mode. That's why the offline computer setup needs an online version of Armory to create the tx for you. It needs to be online to know what coins you have so that it can sign them. Technically, even brief access to a computer able to run online Armory would be sufficient - import your watching-only wallet, create a tx that sweeps your funds to another non-Armory address, then take it to the offline computer for signing.
If you're not even using online-offline split, you can do this with your primary wallet (without any extra steps between creating and signing), but I would try to limit the number of devices that your private keys have touched.