Hi Rick, Thanks for considering all my ideas. I think you are correct that my gun must be a sized for a youth. Based on your experience it is the only answer. I have been trying to imagine shooting accurately from a galloping horse. Maybe they madly rode into a crowd of the enemy and shot at such a short range that they did not need to aim with precision. In this situation the gun need not be held by any particular technique - somehow quickly get the gun pointed and pull the trigger. The target may be just a yard or less from the muzzle. But if the situation did allow for a more careful shot from the shoulder then the sights would be used.
Here is a link to some great photos some showing Moroccan guns being shot from horseback.
http://www.flickr.com/photos/fedala/sets/851624/