Are there wallets that *don't* require downloading the Bitcoin Core, but which let me access the btc in an Armory (i,e., a bitcoind) wallet for which I have a full (16-btc word) paper backup?
If you mean by leightweight wallets that don't require you to download the blockchain, then I'd suggest electrum: electrum.org/#download
If you open bitcoin-qt and click to export your private keys, or use the dumpprivkey command in bitcoind and import that key into electrum (by selecting "standard wallet">"use public or private keys">and input your data there.