It has been ages since I have used throwing weapons, so I may be wrong. Similar to how you need a bow in your ranged slot AND arrows in your ammo slot to do archery, I believe you need a throwing weapon in both the ranged AND ammo slot to do throwing.
So you need at least two hammers. The hammer in the ranged slot tells the game what type of ammo to use (You wouldn't throw your bow if you were out of ammo), and the ammo slot has the ammo you want to consume, in this case another hammer.
I assume both items have to be the same for throwing (unlike archery), like you couldn't have a rusty hammer in ranged and a shattering hammer in ammo, but I could be wrong there. I haven't actually tried that. I generally used shurikens for throwing, so they were both the same item. I remember putting them in both the ranged and ammo slots to throw.
EDIT: Looking at
https://wiki.project1999.com/Shattering_Hammer , which is summoned from the Bracer of Hammerfal, that hammer can be placed in both ranged and ammo slots, with a range of 55. So they can be thrown.
https://wiki.project1999.com/Rusty_Warhammer can only be placed in the ranged slot, with a range of 40, but not the ammo slot. My guess is you can't throw the rusty hammers because you can't put them in the ammo slot too, unless the wiki is wrong about which slots it can go in. Maybe it is just a fluke that it has a ranged value? I would be suprised if throwing worked like archery, where the range calculation uses both the bows range and the arrows range combined.