How to obtain the private key of an Armory wallet? I have a paper backup, a digital wallet backup and all the passwords: how do I retrieve the private key for a watch-only wallet so I can send some coins out of it (created in armory and imported into, for example, blockchain.info)?

If that's not possible, is using passphrase from within armory the only way to send coins out of an armory watch-only wallet?
This is how you obtain the private key for an Armory wallet:

In Armory-Qt, click on Wallet Properties (or in the newer versions, double click on your wallet to open your Wallet Properties), then click Backup this wallet>See other backup options>Export Key Lists then click the button Export Key Lists. Enter your passphrase and Armory will show your wallet's list of public addresses and private keys. If you are --offline or didn't download the blockchain, the list may be empty (Armory thinks no addresses were used), but checking "include unused" will allow you to see the entire list. Note that a watch-only copy of a wallet uses the same private key as the original wallet it was created from.

This is useful if you want to send coins from an Armory wallet without using Armory, for example from an armory wallet address you imported into blockchain.info. In order to do so, you need to enter into the chosen service the private keys to the wallet you want to send from. In the case of BlockChain.info, the key it accepts is the one in PrivHexBE format, after you remove the spaces.

Word of caution: after you enter a wallet's private key into any online service that wallet is no longer secure. You should considering transferring all the coins it holds out - do not use that wallet again.