It can help putting things into a perspective: a lot of people stutter, it's very likely that you are not the only person who stutters on the plane! The hostesses wouldn't mind for sure waiting a second more for you to order, in case you should stutter. The same applies to border agents: they deal with hundreds of people every day, it's very likely they talk with someone who stutters at least once per day, and they know for sure the difference between someone who is hiding something and someone who stutters. Everything will be fine, good luck! :)