To use Armory securely, you need an offline PC and an online PC. On the offline PC you create the wallet and generate a watch-only wallet for your online PC. On the offline PC you don't need to install Bitcoin Core, however on the online PC you do.
Bitcoin Core and downloading the whole blockchain is a prerequisite for running Armory in online mode.
For further details I'd recommend heading to the Armory subforum:
https://bitcointalk.org/index.php?board=97.0Alternatively I'd recommend either getting a hardware wallet for a great mix of convenience and security -- either a Trezor or a Ledger Nano S -- or if security is not that much of a concern try Electrum.