If you haven’t already, i highly suggest that you go to Youtube right now and search for that one Will Ferrell interview where he simply does not know what to do with his hands. It is a question many public speakers have hidden in their minds and it is one that greatly baffles me. I am certain that no one in the world- at least the 10,000 people that i have encountered and worked with- suffer from not having a natural flow or movement in their hands. You most likely do not have flailing, distractive hand movements either, therefore, worrying about what to do with your hands is simply a waste.
The far bigger problem is phrasing the hands, holding pens and remotes, and holding a lectern. What you need to do with your hands is to just move them naturally as you do all day long when you speak. Stop worrying about this nonsense which is in fact not a distraction at all. The possibility of you leaving your hands being distracting like Will Farrell is extremely low, Similar to your chances of getting a multi million dollar movie and comedian offers: very slim.
Let’s worry about the real risk which is that you may end up giving a speech that is so boring that nobody remembers anything. Now that is a real problem.