Trux, thanks for thinking of me.

I do stop shivering at the start of apnea, even if I was shivering before I started. The problem is that if the apnea lasts more than about 2 minutes, the shivering starts again. Also, eventually the shivering at the surface can get so bad that it causes lactic acid buildup, so it is impossible to start a dynamic in a good state.
Maybe there are two problems. One is that I don't have much of a dive reflex, so the shivering does happen during apnea. The other is that any activity, including shivering, causes an unusual amount of muscle fatigue.
There may be many factors involved. When I did some 'freediving' in water of 10-12c, with normal clothes and no suit, I did not get huge spasms of shivering. This could be because the air temperature was warm and it was a sunny day. Getting into a much warmer pool of 25-26c can cause much more shivering if the surrounding air is cold.