It has been shown that humans are the most asymmetric in their handedness - meaning we have about 9 righties to 1 lefty. Dogs, cats, and other animals are very symmetric, not showing a preference for one side or another. From this information, I would say that a dog preferring to shake paws with it's left or right would have no effect on the animal's physical or mental behavior. That being said, I'm not an expert in veterinary science, so there may be an example out there showing contradictory evidence.