Elastostatic cloaking aims to hide an object so that the displacement response is indistinguishable from homogeneous surroundings. Achieving elastostatic cloaking on general shell structures is significant while challenging, as curvature effects complicate the mechanical response and limit established design routes. An explicit topology optimization framework for elastostatic cloaking on shells is developed by integrating a multi-patch isogeometric analysis (IGA) formulation with the moving morphable void (MMV) method. IGA enables exact representation of curved geometries and smooth, high-order discretizations on CAD-defined patches, whereas MMV provides an explicit and compact parametrization of void boundaries, yielding optimization results that can be directly transferred to CAD environments. Cloaking performance is quantified through an energy-based error measure that evaluates the mismatch between the cloaked and reference responses in the surrounding region, and this metric is adopted as the optimization objective. A series of numerical examples demonstrates that the proposed framework is effective for complex shells with hard inclusions or defects of various shapes, and that the optimized cloaks markedly reduce the error measure in the surrounding region. Moreover, the resulting cloak designs remain robust with respect to variations in loading directions. The proposed strategy can be readily extended to cloaking problems in other physical fields on shell structures.