Some monster hunts spawn with more regular foe having already hunted the monsters, and as such usually carrying the parts as dropped loot.
Star gods are highly resistant to both daze and electric type damage, in addition to high melee dodge, so yah running up and whacking them is pretty fruitless.
The wand works by inflicting choke type damage as stun and a small amount of lethal, so it function the same as with any other mixed dmg knockout tool, like handle or pipes.