Elastic gridshells are a class of planar-to-3D linkages typically composed of straight flexible beams connected via rigid rotational joints. The integration of planar curved flexible beams into these linkages significantly broadens their design space, allowing for a diverse range of deployable configurations. We termed these special types of linkages C-shells. The main characteristic of these structures is that they intrinsically encode their deployed states in the shapes of their beams while maintaining a planar and zero-energy assembly state. However, designing a C-shell is not a trivial task due to the freeform shape of their beams and the complex physical behavior emerging from their elastic deformation. To address this challenge, we introduce a computational approach for interactive design exploration of C-shells. We show how we can leverage geometric principles on the arrangement of the beams to efficiently create linkage assemblies that deploy into low-energy states of varied geometries and aesthetics. Our reduced parameterization relies on planar conformal maps that preserve the deployability of a reference linkage while generating a spectrum of smooth design variations. To explore design alternatives, users can interactively modify the beam connectivity, starting from a selection of predefined parametric grid topology families. Our interactive tool includes a physics simulation, offering both visual and quantitative feedback on the deployment of the explored designs. We showcase the utility and adaptability of our approach through design studies of a variety of C-shell families.