Scientists have conducted research which suggests that cats may have paw preferences:
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Psychologists from Queen’s University Belfast in North Ireland, in a study published in Animal Behaviour, conducted a series of experiments on 42 kitties to discover if they are left- or right-pawed.
In two of the experiments, in which the cats had to reach for a toy mouse, the kitties were ambidextrous. But in the third experiment—in which bits of tuna were placed in a jar for a cat to fish out—showed a definite paw preference: 20 out of 21 female subjects used their right paw, and 20 out of 21 male subjects used their left.
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OTOH, I used to have a golden retriever mix that would shake what she was asked, "Right paw" or "Left paw".