More specifically,
Weapon Damage - This attribute effects the amount of damage you do with any skill found in the Weapon Skill Line.
NOTE: It does not matter if the skill uses Magicka or Stamina as long as long as it is a Weapon Skill, it is governed by this Attribute.
So, one can assume one handed and shield is a weapon skill line and the shield dmg would be affected the same way as a one handed.
Please post correction with reference if this is incorrect.
Thanks, and hope this helps