Do you need to specificaly conjure your weapon, or it would work for just projectiles?
How about for example Acid Arrow?
You don't specifically need to
conjure a weapon. Some spells affect the weapon you're holding, essentially allowing you to channel a spell through a melee attack.
Acid arrow wouldn't work because it doesn't involve a weapon. You're still casting the magic from your hands, just like you do for scorching ray, etc.