My Witchdoctor is using shooty/staffy weapons, and the info only said Will boosts weapon damage, but I was wondering if Agility would also increase the weapon's damage in addition to the Shooty weapons talents.

It depends on the weapon. The information about the weapon will tell what ability (Strength, Will, or Agility) will give a bonus (the higher your statistic, the better). As I understand it, no other ability will affect the weapon damage. For example, a Shooty/Staffy weapon that depends on Will would not be affected by your Agility statistic. One way to tell is to equip the weapon and then mouse over the Weapon Damage when you are in the Character Screen (press 'c'). That should show you what is affecting the Damage that you will do when you use this weapon.

One other thing to consider when choosing a weapon is any other information about the weapon. Does is add to Armor, have Armor piercing capabilities, does it affect other statistics, etc.