Welcome to HCM
We understand your concerns
You are healthy at 69, I am very much pleased. At 69 people loose their steam psychologically and turn themelves into self created cocoons. You are different. You have diabetis, but that is not the reason for the present symptom.
Hands freezing and body shaking are symptoms when outside temperature is sub par and body tries to maintain the temperature to ideal. Your condition is similar without the low outside temperature. Apparently no clinical defintions might be available for this.
I might suggest that the symptoms are rather psychological. Before confirming, you visit a general physician and get all the checks done to be sure that there is no other trouble. Then visit a psychologist
for counseling and psychotherapy
. I can help you online if you desire so. Good luck.