Fiber-reinforced composites, owing to their high specific stiffness and strength, are extensively adopted in lightweight and high-performance thin-walled structures. The rapid development of advanced manufacturing technologies, particularly automated fiber placement and fused deposition modeling, now enables fiber tows to be steered along curvilinear trajectories rather than being confined to straight paths. Consequently, composite laminates with spatially varying fiber orientations have emerged, which exhibit enhanced stiffness, strength, and buckling resistance while offering unprecedented design freedom. By tailoring fiber paths to match position-dependent stiffness requirements, the load-carrying potential of composite structures can be further exploited. However, unlike isotropic metallic materials, composites possess pronounced anisotropy, and optimal fiber paths must not only align with the underlying stress fields but also satisfy manufacturing-imposed geometric constraints, such as uniform spacing and curvature limits. Conventional optimization approaches developed for metallic shells or two-dimensional planar structures become inadequate when applied to three-dimensional composite shells. A fundamental challenge lies in constructing an effective parameterization framework capable of representing fiber paths on complex surfaces while incorporating manufacturing constraints. To address this issue, the present study proposes a level-set-based optimization method for composite shells. Radial basis function interpolation is employed to define the level set function for each layer, and a conformal mapping strategy is developed to transfer contours from a two-dimensional parameter domain onto a three-dimensional curved surface, facilitating an accurate and flexible representation of fiber layouts. Two crucial manufacturing constraints are explicitly formulated from the gradient norms and contour curvatures of the level set functions. A stiffness maximization model is then established. Numerical examples involving representative engineering shell structures demonstrate that the proposed method effectively generates manufacturable designs while significantly improving structural mechanical performance. The framework provides a general methodology for the concurrent consideration of anisotropic material behavior, complex geometry, and process feasibility in composite shell optimization.