This works, I’ve tried it too. Also, when I exhale slowly as I’m speaking, I don’t stutter till i’m out of breath. The whole sentence comes out easily. But accidentally if I stop and take a break and continue, I stutter. So I try to take a really deep breath and use it till the sentence gets over. Then repeat for the next one without any break in between the sentence. Try practicing this and it’ll become a habit and you don’t have to consciously do it :) hope it helps.