Why should armor on shields work different from body armor?
Against zero armor every damage type should be equally effective. At somewhere around 15 armor all damagetypes are nearly equal. The more armor you have the better pierce and blunt get.
But since bonus against shield greatly increases the damage, it's mostly the best choice to use an axe.
If the damage of your cut weapon is the same as of a blunt weapon and neither of them has bonus vs shield you should prefer the blunt weapon...
If the enemy has enough shield skill it doesn't matter if you use pierce, blunt or cut. If you don't have bonus vs shield it takes forever to break the shield.
You should look for bonus vs shield, most damage, blunt, pierce, cut in this order