If I am the only player (or the last player in multiplayer) and only the only enemy engaged is engaged with me, can I still ready my defender with his Armored Destrier even if there are no shadow cards to discard from enemies engaged with the defending player (me)?

Yes, because Destrier says to ready the hero first. So, you can still ready the hero without discarding the shadow card. However, I think if you couldn't ready the hero for whatever reason (a treachery or shadow card effect), you would not be able to discard another shadow card.