This seems to be different depending where you look.
If you put the weapon in the right side for the on-screen interface it says right hand in the stats screen. Which even though the pic faces you is how it should be.
For the picture in equipment tab, it is in left.. although it is the right side.. it should probably be left side for right hand for this.
When adding "clothes" the protection stat did not change until I swapped the equipment with another character. (only happened once early in the game though, not sure how to reproduce).