Breathing is an involuntary function. We're not usually aware of it. But sometimes, when we're lying in bed, trying to fall asleep, doing yoga, or recovering after a strenuous activity, it becomes the focus of attention. Do you ever think: "Wow, I'm exhaling pretty hard?" I'm betting you don't.
When I'm reading, the word "exhale" always strikes me as medical, drawing attention to itself. Sometimes the phrase "breathed out" is used instead. Or characters "let out a long breath". In some stories, characters talk or think to themselves, "breathe" or "deep breath" in stressful situations. Any of these alternatives work better for me (though my panel of kid readers mentioned that the last one especially bugs them). My best solution is to try not to refer to breathing at all, unless absolutely necessary.