It's good you don't want to overreact, in the sense thst you don't want to make the child more self conscious about their stutter by exhibiting a negative reaction to it or communicating that stuttering is bad. It's not bad or wrong, but there are ways to do it without struggle. But they are already showing frustration and a look of desperation trying to get works out getting them to a good SLP trained in stuttering who understands what to do and won't just work on unhelpful fluency tools is what I would recommend. You should know that stuttering is the area SLPs have the last confident with so it's not like going out and finding a pediatrician. The the difference in SLP quality for stuttering can be large and can make a real difference so I'd encourage some research. See who's near you. Reach out to the NSA or stuttering foundation other reputable groups for recommendation.