Maybe something like this?
There are a finite number of shouts in the game. You could go through the list and assign each an effect strength according to their strength in the game, or as you see fit given the effect. Something like
Effect: Force Push
Fus - 2
Ro - 2
Dah - 2
For each word used in a shout the effect strength adds up, so for the above, all three words would be a weapon 6 force push, or a 6 shift maneuver.
Skills involved:
Discipline: Control the effect and aim just like the magic rules. Not sure exactly how to handle failure to control since it wasn't really a part of Skyrim.
Lore: Allows one complete phrase to be known for each point of Lore. Superb Lore grants 5 phrases immediately. Each word learned after that requires research and possibly quests depending on the effect.
Cooldown: Maybe an exchange for each word used, or possibly just assign a number of exchanges to each shout when you do the weapon ratings.
Rather than using the cool down, you could tie it to mental stress just like the normal magic rules. If you do that, it would likely just be a reskinned evocation. Maybe just have each shout act as an element and add new shouts with refinements.
Just some thoughts off the top of my head. More experienced minds could really help you nail these down if you like the ideas.