Heavy throwing axes are the perfect sidearm for 1h. Loom them to +3 and get 4-5 power throw; they will 1-shot peasants, 2-shot archers, and 3-4 shot anyone in less than plate. Headshots are surprisingly common and will one-shot most people that don't have a heavy helm.
Also, the melee secondary mode is highly effective for shieldbreaking and just surprising people (you can switch from throwing mode to melee mode while your throw is chambered; this confuses the hell out of people and often allows a free hit). The short length makes the melee mode very nice in close quarters or on top of a ladder in siege where you don't want to hit teammates with your backswing.
Crossbow is an option too, but throwing just has more synergy with 1h/shield (you can throw with a shield equipped, and you can make good use of the melee secondary mode of throwing axes). Crossbow is probably better for Battle, and throwing is probably better for siege (I assume; I haven't played battle in like 10 gens, I only play siege).