We automate soft robotic hand design iteration by co-optimizing design and control policy for dexterous manipulation skills in simulation. Our design iteration pipeline combines genetic algorithms and policy transfer to learn control policies for nearly 400 hand designs, testing grasp quality under external force disturbances. We validate the optimized designs in the real world through teleoperation of pickup and reorient manipulation tasks. Our real world evaluation, from over 900 teleoperated tasks, shows that the trend in design performance in simulation resembles that of the real world. Furthermore, we show that optimized hand designs from our approach outperform existing soft robot hands from prior work in the real world. The results highlight the usefulness of simulation in guiding parameter choices for anthropomorphic soft robotic hand systems, and the effectiveness of our automated design iteration approach, despite the sim-to-real gap.