Here are some tricks to speed up and to be accurate and stop the shaking. May they work for you.
Be accurate with your base coat and no touching the skin, but apply it quickly and thin as you like. The slower you go the worse it will be for you.
Be as careful as you can be, and take your time, and paint your first coat of colour perfectly. Straight edges and nicely curved eponychium line, but you do not need to try and get full coverage with this coat and the polish can look streaky.
(here is where you can really speed up)
Apply your second coat super fast. Use a little more polish on your brush, and just paint down the centre of the nail without worrying about going all the way the the very perfect edges you have created! No one will ever see that you have not gone all the way to the very edge and you will not build up any bulk at the edges where clients will be tempted to pick.
Top coat should be super fast to apply as well, as it is clear and you need to cover all the way to the edge of the base coat. Your top and base should be the bread of the sandwich and encapsulate the colour.
You MUST be positioned comfortably and place your clients hand at the angle you need so that your brush feels just like a pen in your hand and the hand is the piece of paper on which you are going to write. You cannot work at your best if the client's hand is straight in front of you ... It must come in at a slight angle, otherwise your elbows will be all bunched up at your sides and you will be cramped and not free to move.
Your elbows should both be away from your sides and at right angles to your body and resting on your desk.
Finally .. balance point positioning ... your painting hand should be steadied and balanced on one of the fingers that is holding your clients hand, and then you will not shake at all. OH ............... and finally, remember to breathe!!
HTH