This paper introduces a differentiable ray-tracing based model that incorporates aberrations and distortions to render realistic coded hyperspectral acquisitions using Coded-Aperture Spectral Snapshot Imagers (CASSI). CASSI systems can now be optimized in order to fulfill simultaneously several optical design constraints as well as processing constraints. Four comparable CASSI systems with varying degree of optical aberrations have been designed and modeled. The resulting rendered hyperspectral acquisitions from each of these systems are combined with five state-of-the-art hyperspectral cube reconstruction processes. These reconstruction processes encompass a mapping function created from each system's propagation model to account for distortions and aberrations during the reconstruction process. Our analyses show that if properly modeled, the effects of geometric distortions of the system and misalignments of the dispersive elements have a marginal impact on the overall quality of the reconstructed hyperspectral data cubes. Therefore, relaxing traditional constraints on measurement conformity and fidelity to the scene enables the development of novel imaging instruments, guided by performance metrics applied to the design or the processing of acquisitions. By providing a complete framework for design, simulation and evaluation, this work contributes to the optimization and exploration of new CASSI systems, and more generally to the computational imaging community.