Manipulating deformable and fragile objects remains a fundamental challenge in robotics due to complex contact dynamics and strict requirements on object integrity. Existing approaches typically optimize either end-effector design or control strategies in isolation, limiting achievable performance. In this work, we present the first co-design framework that jointly optimizes end-effector morphology and manipulation control for deformable and fragile object manipulation. We introduce (1) a latent diffeomorphic shape parameterization enabling expressive yet tractable end-effector geometry optimization, (2) a stress-aware bi-level co-design pipeline coupling morphology and control optimization, and (3) a privileged-to-pointcloud policy distillation scheme for zero-shot real-world deployment. We evaluate our approach on challenging food manipulation tasks, including grasping and pushing jelly and scooping fillets. Simulation and real-world experiments demonstrate the effectiveness of the proposed method.