It would probably make more sense, and be easier legally, to get depleted uranium weapons classed and banned as chemical weapons, rather than nuclear weapons.
The military’s stated reason for using DU is for armour-piercing munitions, because of DU’s great hardness and high density. Given the enormous stockpiles of true depleted uranium, this reason provides no excuse whatsoever for using “dirty DU”. But actual DU should still be banned because of its chemical toxicity, especially as some is vaporised and some becomes an aerosol when DU munitions hit armour plating, their intended target, leading to uranium being inhaled.
“Dirty DU” is a misnomer (part of the attempt to spread confusion, in my opinion). Depletion (of U235) is the other side of the coin to enrichment. “Dirty DU” hasn’t been depleted; it’s a by-product from the reprocessing of “spent” nuclear fuel.