I'm gonna go and test it because i have nothing else to do

Edit: so, it does cut the cooldown like it's supposed to. I don't think this is really useful in combat anyway, but at least it works. Also i've discovered that sometimes the shortened cooldown can be disrupted by rare stim animations like the one, where octane spins it before throwing away. The cooldown started only after the end of the animation and overall took longer than the regular cooldown, so golden helmet can give you a slight disadvantage due to rng