It doesn't add +Skill to your character, like a piece of equipment would.

This is likely due to how offhand skill is handled, if you have a offhand axe with less + Weapon Skill then you receive less attack and accuracy for your offhand. but if it added to your +Skill in the menu it'd show up as +400, when in actuality it's the equivalent to +200 on your main hand and +188 on your offhand.