The idea is unfortunately a bit overused (especially since it has been done before), but I still like the idea - Zombies are effectively scavengers, so it makes sense that they want to pick up weapons. As a second mechanic, I actually suggest weapon durability and reduced weapon drop rates - This could add some balance since now you have to constantly switch weapons. This could leave a scenario where you are weaponless, but I think that's fair since there has to be some difficulty. Also, another improvement I suggest is making it so the direction you slash is where your mouse is pointing.