We present the open-source software package, SHORYUKEN (Streamlined High-level Operations in Real-space to Yield, Understand, and Keep Exchange in Nanowires), for calculating nonlocal exchange interactions in nanowires with arbitrary geometries, sizes, doping densities, and compositions. In addition to enabling new calculations of nonlocal exchange, the SHORYUKEN software package is a significant enhancement of our previous HADOKEN code and includes new algorithmic improvements as well as an improved treatment of surface states for nanowires with intrinsic polarization. Our calculations show that the inclusion of nonlocal exchange can have significant effects on the eigenenergy spectrum, number of occupied states, and distribution of electrons within these nanosystems. The open-source SHORYUKEN software package is the first open-source code for calculating nonlocal exchange to predict electron gas formation in nanowire systems with arbitrary cross-sectional geometries.