Aquatic creatures exhibit remarkable adaptations of their body to efficiently interact with the surrounding fluid. The tight coupling between their morphology, motion, and the environment are highly complex but serves as a valuable example when creating biomimetic structures in soft robotic swimmers. We focus on the use of asymmetry in structures to aid thrust generation and maneuverability. Designs of structures with asymmetric profiles are explored so that we can use morphology to 'shape' the thrust generation. We propose combining simple simulation with automatic data-driven methods to explore their interactions with the fluid. The asymmetric structure with its co-optimized morphology and controller is able to produce 2.5 times the useful thrust compared to a baseline symmetric structure. Furthermore these asymmetric arms are validated on a robotic system capable of forward swimming motion while the same robot fitted with a plain feather is unable to move forward.