What I would do would be to make a secondary wallet somewhere, e.g. an SPV wallet, an Electrum wallet or something like that.  Bring that wallet with you on your trip (or encrypt it and drop it in dropbox - that is not good security, but odds are that you will never use the wallet).  Make and sign a transaction moving money from Armory to the new wallet, but do not broadcast it.  You can even sign multiple transactions of different sizes, although you may not be able to use more than one of them if they use the same inputs.  Encrypt the transactions, leave them on dropbox.   Write down the first address of the Electrum wallet, and an empty address of your Armory wallet. 

If you need to access your BTC on your trip, download the Electrum wallet.  Check that the bitcoin address is as expected.  Decrypt the selected armory transaction and broadcast it using blockchain.info or another such online tool.  When your money appears in the Electrum wallet, spend the part that needs spending, and return the rest to the Armory address you brought along.

Important:  Before leaving, try this out at least once.  Mistakes can potentially be expensive