Neutron-induced reactions with charged particle emission play an important role in a variety of research fields ranging from fundamental nuclear physics and nuclear astrophysics to applications of nuclear technologies to energy production and material science. Recently, the capability to study reactions with radioactive targets has become important to significantly advance research in explosive nucleosynthesis and nuclear applications. To achieve the relevant research goals and study (n,x) reactions over a broad neutron beam energy range, the Low Energy Neutron-induced charged-particle (Z) chamber (LENZ) at Los Alamos Neutron Science Center (LANSCE) was developed along with varied ancillary instrumentation to enable the aforementioned research program. For the (n,x) reactions of interest at low energies, a precise simulation of the discrete spectrum of emitted charged particles is essential. In addition, since LANSCE is a user facility, a simulation application that can be easily accessible by users has high value. With these goals in mind, we have developed a detailed simulation using the GEANT4 toolkit. In this work, we present the implementation and the validation of the simulation using experimental data from recent campaigns with the LENZ instrument. Specifically, we benchmark the simulation against a similar MCNP-based tool and determine the realistic range of applicability for the probability biasing technique used. We describe our implementation of an evaluated library with angular distribution and partial cross-section data, and we perform a validation of the application based on comparisons of simulated spectra with the experimental ones, for a number of targets used in previous experimental campaigns. Last, we discuss the limitations, caveats, and assets of the simulation code and techniques used.