First of all, fucking kudos to you man. You went for a nerve raking interview, you stuttered a lot which is always embarrassing and gives the worse feeling, but you came back an hour later and killed it! That in itself is an achievement! Bravo! Next, if you feel as if you will be confident on the job and the more comfortable you are there aka the longer you are there and make rapports will decrease your stuttering, then that's a definitely a good sign. That should be a pretty viable reason to go through with it and explain to him that as time progresses and the more comfortable you feel, the better things get. Nice work!