Supernova (SN) feedback plays a vital role in the evolution of galaxies. While modern cosmological simulations capture the leading structures within galaxies, they struggle to provide sufficient resolution to study small-scale stellar feedback, such as the detailed evolution of SN remnants. It is thus common practice to assume subgrid models that are rarely extended to low metallicities and that routinely use the standard solar abundance pattern. With the aid of 1D hydrodynamical simulations, we extend these models to consider low metallicities and nonsolar abundance patterns as derived from spectra of Milky Way stars. For that purpose, a simple, yet effective framework has been developed to generate nonsolar abundance pattern cooling functions. We find that previous treatments markedly over-predict SN feedback at low metallicities and show that non-negligible changes in the evolution of SN remnants of up to 50% in cooling mass and 27% in momentum injection from SN remnants arise from nonsolar abundance patterns. We use our simulations to quantify these results as a function of metallicity and abundance pattern variations and present analytic formulas to accurately describe the trends. These formulas have been designed to serve as subgrid models for SN feedback in cosmological hydrodynamical simulations.