It can cause damage. Whispering does put a strain on your voice that normal speaking does not. However, I understand what you mean. Whispering seems to trigger a different way of speaking - as if we're speaking to ourselves or to a child or animal. I would work on trying to flow from a whisper to a normal speech within a word or sentence. Ease yourself into it. I have a bad habit of putting "Ha" sounds infront of words, so much so that if I am saying my name, people repeat it back with the "ha" sound. I think it's better to focus on becoming confident and not allowing the stuttering to keep you from speaking your mind than not stuttering. For me, stuttering is part of my voice and while I encourage speech therapy and finding ways to work through blocks and repetitions I don't want to cure it.