You can use a Light client that doesn't require the full blockchain, eg: the popular Electrum wallet.
Just follow this to be able to export your address' private key from Armory to Electrum:
Click "
Wallet Properties" then, "
Backup This Wallet".
Check "
Export Key Lists", then the button with the same name below, type your password and a window will open.
Check "
Include Unused (Address Pool)", check "
Omit spaces in key data" (
below) and find your address from the list and copy its private key WIF (
PrivBase58).
Download Electrum from the official site:
electrum.orgUse, "
Import Bitcoin addresses or private keys" when creating a new wallet, and paste your private key there.
I recommend you to verify your downloaded Electrum before importing the private key to be safe,
using these instructions:
https://bitcoinelectrum.com/how-to-verify-your-electrum-download/