The purpose of writing this paper is: The low-energy $\gamma$-ray (0.1-30 MeV) sky has been relatively unexplored since the decommissioning of the COMPTEL instrument on the Compton Gamma-Ray Observatory (CGRO) satellite in 2000. However, the study of this part of the energy spectrum (the ''MeV gap") is crucial for addressing numerous unresolved questions in high-energy and multi-messenger astrophysics. Although several large MeV $\gamma$-ray missions like AMEGO and e-ASTROGAM are being proposed, they are predominantly in the developmental phase, with launches not anticipated until the next decade at the earliest. In recent times, there has been a surge in proposed CubeSat missions as cost-effective and rapidly implementable ''pathfinder" alternatives. A MeV CubeSat dedicated to $\gamma$-ray astronomy has the potential to serve as a demonstrator for future, larger-scale MeV payloads. This paper presents a $\gamma$-ray payload design featuring a CdZnTe crystal calorimeter module developed by IDEAS. We report the detailed results of simulations to assess the performance of this proposed payload and compare it with those of previous $\gamma$-ray instruments.