Well they could have an animation like in Rome: Total War. Would that work?
Never played the game, but think about it this way: when you run with a weapon, it stays together. Your long sword isn't going to wobble around like jelly. This is because weapon models in game are designed as solid objects. These objects are static.
Enter the sling.
A sling is pretty much a strap of leather with an appropriately sized fitting area for your rock. Leather is NOT solid like a metal sword or a polearm. Leather is flexible and reacts to gravity. It is dynamic.
Warband does not handle dynamic weapons. There are no weapons currently that are dynamic.
Is it impossible to program in dynamic weapons? During the later stages of beta, taleworlds purchased the rights to the Havok physics engine. This is the same physics engine used in Halo 3 and Half Life 2. The Havok engine does support dynamic weapons. However, a lot would need to be done to implement it into warband.
Taleworlds did not program in these weapons because of the sheer number of manhours it would take to implement it into their game. It is not a simple change of attack animation. This would require new running physics (leather bobbing when they run,) new hit animation (what happens when they get hit with they are using the weapon?) and block animations. This would require the sling reacting to gravity and the environment around the player.
Making dynamic weapons in warband would require an entire team in itself to implement. I doubt chadz is willing to do that by himself.