Do weapons and spells in the off-hand suffer from reduced effectiveness?
The Dragonborn is ambidexterous, but refuses to wield a shield in their right hand. Magic and weapons can be used in any combination of Right / Left, Left / Right, etc.
The Dual-Wield "penalty" as it were, is that you cannot block when dual-wielding. (Even though you could normally block with a single weapon if your offhand is free.)