Are there risks if the side joystick must be handled with a pilot's weaker hand? Suppose that a first officer were left-handed and a captain were right-handed. Both are NOT ambidextrous. Even after training, what if their weaker hands' control and  degree of versatility
remain worse than their dominant hands'? 

In other words, in commercial (and not just military) cockpits, joysticks (on the side) must be grasped with only one hand. But does this fact presuppose or require perfect ambidexterity?
I can't speak for all pilots everywhere, but I've flown both sticks and yokes from both the right and left seat (as well as the front and the back seat in tandem aircraft) and found the adjustment process between switching from right to left hand to be very quick. I found getting used to sight picture differences to be a much bigger challenge and, like many others before me, sideloaded my first few landings (along with climbing/descending during turns) until I got the hang of it. 

Other pilots I've spoken to about this have expressed the same feelings; there is a learning curve, but it is by no means insurmountable. At any rate, flying is far more of a mental activity, with masterful physical coordination being surprsingly far down the list of innate qualities a pilot needs. 

And no, I am not nearly ambidextrous; in fact, my coordination abilities with my non-dominant hand are hilariously poor, as anyone who's ever watched my try to toss a tennis ball during a serve can attest.