First of all, don't think you're out of the line with anything you said. I find it admirable that you're trying to find solution to work better with your coworker, kudos to you. Telling someone to slow down and breath is probably worst possible thing you can say, we are all aware of that and been said same thing whole life, it usually doesn't help too much. I'd say you have to go by the ear. If you see he's really struggling and is frustrated you can do something like "Oh, you mean .... ?" and put in whatever you think he was trying to say. Other times when it's not that bad just wait for him to say it. One thing you can maybe do, is try one of those for a few times and then openly ask him if he finds it annoying when you finish his sentences, etc. In my experience, bringing up subject with someone can be unpleasant, but once you talk about it, he'll end up being way more relaxed around you and it will probably help with his stutter as well. I feel like I haven't said much, but now that I thought of it, I really don't see universal solution.