Since you hit with your fist, arm, and even whole wrist, more or less yes, you exhale through your nose (Never through your open mouth!!). I take it you are also contracting heavily your diafragm muscle (The one responsable for breathing) to increase the rotation of your body in order to lengthen the reach of your arm, but ultimately you NEVER open your mouth, much less scream, because that could get you into deep trouble if you receive a hit at the same moment. Ali's jaw got broken more or less due to having his mouth half-open when he landed a heavy punch by Joe Frazier.
If I try to re-create the sequence of punching and try it both silently and screaming, I think that in the second one I loose strength in the punch because part of the strength comes from the fact of having your lungs full of air and your diafragm contracted to hold the air there. When letting all that air loose the muscles get relaxed and I loose strength in teh final part of the strike.
Again, take that with a grain of salt because boxing is a fighting sport that is quite different to other fight techniques, but ultimately I have NEVER seen any professional boxer sream while punching, and if that was better, I guess they would have found it out and practiced it.
