If you can get to your offline wallet Armory (physically and past its password/s) - you have access to your private keys.
Worst case, urgently needing funds:
In the offline Armory, under 'Backup Wallet' you can get a list of the private and public keys for each address. This enables you to copy one or a few addresses that have sufficient coins to a plaintext file and import it to another client wallet.

To greatly decrease the 'attack surface' of a paper backup breach Armory has Fragmented Backups. You can use M of N scheme where you plant these N backups in different physical locations and need M of them to recreate the wallet.