The 'battle' would be interesting.
What is the shooting range,anyway?
Maybe you can stuff the arrowhead with cotton wool, then wrap with cloth to minimize the damage.And everyone,slingers and archers,wear some kind protection,i.e. goggles,helmets,neck protection,hats,etc.
I think it's not fair for slingers as bouncy balls won't fly as far as lead and stones.