A steady hand begins with a steady interpretation.

How steadily you act follows from how you have read the situation. If your interpretation is that everything is falling apart, your hands will move accordingly, and no amount of trying to appear calm will fix an unstable reading underneath. Getting the interpretation right and proportionate is what actually settles the behaviour.

When you notice yourself becoming shaky, look at the story you are telling about what is happening. Ask whether it is the most accurate available account. Correcting the reading tends to steady the hands more reliably than trying to steady them directly.