Look up "Essential Tremor". My husband has this. He does okay in everyday life stuff, but shakes after exertion. After trimming the hedges with an electric hedge trimmer he shakes so badly that liquid spills out of a glass even with a two-handed grip.
Not much to worry about - isn't deadly or anything. Tends to be familial. You might casually ask about family members having this. My husband's father has it also.