To unlock the High caution trophy in World War Z, you will need to complete a level without dealing any friendly damage.
It is extremely easy to accidentally shoot one of your teammates during the heat of battle, so probably the easiest way to unlock this trophy is to play on the easiest difficulty as a pacifist and not shoot anything.
You can combine this trophy will the trophy for only using your pistol during a level. Kill one zombie with the pistol at the start when you are 100% certain that no friendlies are going to get in the way, finish the level playing as a pacifist and you'll unlock both trophies at once.