If Vasher is an Awakened, how could he give away his Breath with a normal command and not die, if giving away Returned breath makes them die?
He doesn't give away his Divine Breath; but he has a store of regular breath which can be used the same as any other awakener.
We see this happen at least one other time in Warbreaker, after Susebron is healed, he begins to awaken other objects without any loss of his Divine Breath. In fact, that was the purpose of the store of breaths that Vasher had left with the God Kings (or more specifically, with the priests who administer the returned). He gave a large store of breaths to a returned for the express purpose of a mass-awakening.
Now, that obviously only addresses half the issue here, because in Warbreaker we don't just see Vasher use awakening without giving away his Divine Breath, we see him give away what appears to be all his breath, becoming a Drab. This obviously takes a little more explaining, and thankfully Brandon Sanderson and the asker JEREMY_CARROLL have done all the work for me:
How could Vasher become Drab, since he would have to give up his Big Breath to do so?
The Divine Breath can be hid. Essentially, you have to view yourself NOT as a god at all, using a very specific bit of mental gymnastics. As a Returned, your body changes based on how you see yourself. (This, by the way, is an indication that Lightsong was more pleased with himself than he ever let on.)
You don't lose your Divine Breath, but it does go into hiding, making you look like a normal person. But you're still Returned, and are consuming a Breath at one a week. If you give away your other Breaths, you retain this hidden one, but your body will still consume its own spirit if left to do so. So you still need a Breath a week to survive, and will die the week you don't get one.
Basically, Vasher gave up everything except for his Divine Breath, and through his ability of suppressing his Divine Breath, this makes him functionally a Drab until he unsuppresses his abilities (or dies if he does not get an additional breath within a week).