The ingame description for those armors says that they don't stack with cards. After testing a bit, it seems that the card effect overwrites the original element of the armor, i.e. if you have Lucius's Fierce Armor (Fire), you take lots of damage from ice and water spells, however if you put a Swordfish Card (Water) into it, the damage is reduced as if you were just wearing a normal Swordfish Mantle.
So, to your original question, you'll only get shadow element reduction/Bathory card effect, not the extra wind reduction.
