So, yeah, perhaps some will hate this, but here goes;
Dwarves arent savages. Sure they like axes, and are seen throwing them sometimes, but they have discovered the art of archery, as also seen.
My suggestion is to replace the dwarven axe throwers with dwarven archers. And keep the throwing axes, and give them to dwarven warriors, to use like some units use spears, a ranged attack before getting into melee range.
Now, how can a short dwarven bow compare to the bows of men, elves and orcs? By the wonder of dwarven steel my friends! Dwarves are nothing but stout! So making bows of metal, so they can achieve the same force upon impact, and the same range despite their smaller size. Now, bows of wood may be cheaper, so why bother with dwarven stuff? As I said, they are stout. Durability. Metal is more durable than wood right?
So, make a new dwarven weapon, using dwarven steel rather than wood, with comparable damage and range, but higher durability than wooden counterparts. And revamp dwarven units, make ranged units archers with the new bows, and give warriors 1-2 throwing axes to use like spear soldiers use spears.
Not an unreasonable idea, right?