Using a heavy armor shield would contribute to the heavy armor skill (I would assume), but the perks that would be in effect would vary. Most heavy armor perks need you to be wearing all heavy armor (by which this means helmet, boots, gloves and chestpiece).
The Juggernaut perk (of which there are 5 levels) increase the armor rating of any piece of heavy armor regardless of what other pieces are equipped. This means that you can wear all light armor and still have a heavy armor shield that benefits from Juggernaut.