This post describes the steps on how to export the keys from your Armory and two replies below it has an example import process to Electrum.

Link: https://bitcointalk.org/index.php?topic=4746784.msg43255691#msg43255691
The provided images no longer updated since the user is a bit inactive but the post itself should be easy to follow.

And yes, you certainly need Armory to be able to export the keys but you don't need it to be active during import to the wallet of your choice.