Your hands can shake while your voice stays steady. People only hear the voice.

Physical nerves and visible composure run on separate tracks. Your body can do whatever it likes while the words come out level, and almost none of the internal turbulence reaches the room. You experience it from the inside at full volume, which is why it seems so obvious to you. Everyone else gets the voice.

Before the next thing that frightens you, stop trying to eliminate the shaking and put your attention on pace and volume instead. Speak slower than feels natural and finish your sentences. Let your hands do whatever they are going to do.