Matthew,
There's nothing to 'register'. The validation logic is baked into the ShoppingCartInfoProvider class.
However, you can customize the behavior of many methods for Xperience's built-in types, like ShoppingCartInfoProvider.
Here's an example of customizing the OrderInfoProvider. The process is identical for ShoppingCartInfoProvider. You will want to make sure that customized code is referenced by both the Administration application and Live site application.
You'll want to override protected virtual IEnumerable<IValidationError> ValidateShoppingCartInternal(ShoppingCartInfo cart) which uses the ShoppingCartValidator on the cart and ShoppingCartItemValidator on each item in the cart.