you mean like a spell? All shouts are actually spells that equip in the "voice" slot from what I've seen in the CK...Look under spells and put "voice" in the filter...copy the one you want to duplicate, and change it's type should work...or just put the effects that are in the shout spell and put them in another spell.
What's strange is that the effect for shouts don't do anything beyond a visual effect. For example if I duplicate sprint, rename it and add it to my character. It just flashes the effect of the Shout but it does not push my character forward. There is no script that I see associated with it so maybe Shouts are handled by the engine in some other unique way?