A character attempting a close combat attack without a proper weapon (either unarmed or wielding an improvised weapon) can make a brawling attack:
Brawling attacks are made using the Dagger weapon skill, causing 1 Endurance point's worth of damage on a successful roll, and additional harm equal to the attacker's Damage rating on a great or extraordinary success. A brawling attack cannot result in a Piercing blow.
I'm trying to adhere to these guidelines, which would not normally apply to a weapon such as a sling or stave (or a sling-staff, for that matter). Or, if it does apply, does not allow for normal damage or any Injury from matching or exceeding the weapon's Edge. The weapon must be treated as an improvised weapon until the bearer is trained in that specific weapon-type's use. Without such training the weapon can never do more than 1 point of Endurance damage on a normal success. This is regardless of how you think the weapon should be statted.Throwing Attacks
A character attempting a ranged attack using a stone or another object not specifically designed for throwing makes a throwing attack:
Throwing attacks are rolled using the Dagger weapon skill, and inflict 1 Endurance point's damage on a successful role, and additional loss of Endurance equal to the attacker's ranged Damage rating on a great or extraordinary success. A throwing attack cannot result in a Piercing blow.
Now, maybe you are trying a home-brewed rewrite of the above rules that negates what I wrote and I just don't understand your version. But, if so, you haven't convinced me that we need such a revision or that it works well. I'm willing to pay attention if you want to try to clarify your position.