You can restore a wallet from the root key and then generate and export the private keys from there to be imported into another wallet. However doing this requires you to know how many addresses that wallet used. Otherwise you may not receive all of your Bitcoin.
Start Armory in offline mode. Then use the "Import/Restore wallet" button and follow the wizard to restore the wallet. Once that is done, open the wallet properties and choose "Backup this wallet". Then choose the option "Export Key list" and you will get a list of all of your private keys from that wallet. Note that you may need to extend the wallet keypool or click the "Receive Bitcoin" button a lot of times in order to get all of the addresses you have used.
Can I do this even if I have an Armory client that won't start until I have downloaded a couple of gigs of Blockchain?
