I remember experimenting with high shield skill and different shields like a plate covered round shield. To my surprise, the plate covered round shield broke fairly easily to a bonus-against-shield weapon, but shields with much less armor but higher health took more hits.
Disclaimer: the following is anecdotal, so take this speculation with a barrel of salt
So if a high armor / low hp shield broke easier than a low armor / high hp shield, both with high shield skill (ie 11-12) then that leads me to believe that shield skill's % reduction in damage applies after the effect of shield armor. Consider the following hypothetical situation (and speculative assumptions about how shield armor works)
Let's say an attack will deal 200 damage, and the plate covered round shield's armor will mitigate 61 of that (again, this probably isn't how it works... just making up a situation for speculative purposes). The plate covered round shield will take 139 damage, which will be deducted from its shield health of 178. This is before shield skill reduction, which we'll get to in a moment.
Let's take the same attack and apply it to the elite cav shield, which has 21 armor and 250 health. The elite cav will mitigate 21 and take 179 damage.
Now let's apply shield skill reduction, assuming a shield skill of 11 (which reduces damage to shields by 88%).
The plate covered round shield now takes 16.68 damage, while the elite cav shield takes 21.48 damage.
Thus the plate covered round shield will take (178/16.68 =) 10.67 hits to break, while the elite cav shield will take (250/21.48 =) 11.64 hits to break.
This supports the general anecdotal evidence that high hp/low armor shields take more hits to break than low hp/high armor shields when the attack does sufficient damage (ie anything with bonus against shields or just high damage cut weapons, etc)
But let's consider the opposite order of operations, and apply 11 shield skill % reduction first to a 200 damage attack. The attack is reduced to 24 damage. If the plate covered round shield's armor effectively "soaks" in operation, then the plate covered round shield should never take damage with sufficient shield skill, because of its high shield armor. But that's fairly easy to disprove, considering that you can hit a plate covered round shield and 11 or even 12 shield skill with an axe and eventually break it.
TL;DR It seems to me that shield skill % reduction applies after shield armor's contribution to damage mitigation.
