If you don't have the connection or disk space to download the whole blockchain, it'd be best if you use SPV wallet instead such as Electrum.
On Electrum all you had to do is to connect to Bitcoin Node and download the latest header, which is only a few megabytes.
I'm sure you can import Armory wallet into Electrum easily in just a few clicks
Private keys will need to be exported and then imported/swept into Electrum. Relatively easy since the address is P2PKH, but Armory doesn't use the same wallet format as others, making it a bit more complex.