I think it is a neuromuscular problem. try taking a break after your first flight, and holding the transmitter in a different position. Try to see if it is positional.
As light as the tx is, you may actually be getting muscle fatigue from standing in the same position. You can try some weight training.
First try moving around, and moving the position you are trying to hold the tx in.
If it continues to get worse, see a doctor. I am not kidding.
It is likely nothing.
I know this because I have had some neuro damage in the past.
I get shakes in my left hand when I am coming in for a landing. However for me, I know what it is. It is the neuro damage coupled with holding my thumb and body in the same position.
Some training will probably alleviate the problem. I don't mean this as a cut, but it could just be you are a little "weak" in that position, and your body gets fatigued.
Think of yoga, and how fatigued people get when standing in the same position... If you don't know about yoga, ask someone, or try it and you will see.