What? No math?
Not when Arvin already has the answer in hand...
I'm too busy at the moment to run numbers for OP, but it would be the more precise way to do it. The calcs are basic structural work and not too involved.
What would be the minimum dimensions for absolutely no bending movement there?
No matter how thick you make it there is always deflection under load, it just gets hard to see or measure. You have to define how large the deflections can be and still be considered 'stiff'. This is something that needs calculation if you want a precise answer, but I would say making the handle area 2.5-3x as thick as the base of the limb will get you in the ballpark.
Mark