Galaxy cluster mergers are a powerful laboratory for testing cosmological and astrophysical models. However, interpreting individual merging clusters depends crucially on their merger configuration, defined by the masses, velocities, impact parameters, and orientation of the merger axis with respect to the plane of the sky. In this work, we investigate the impact of merger parameters on the X-ray emitting intracluster medium and gravitational lensing maps using a suite of idealised simulations of binary cluster mergers performed using the GAMER-2 code. As a test case, we focus on modeling the Bullet Cluster-like merging system Abell 2146, in which deep Chandra X-ray and lensing observations revealed prominent merger shocks as well as the mass distribution and substructures associated with this merging cluster. We identify the most interesting parameter combinations and times and evaluate the effects of various merger parameters and viewing direction on the properties of merger shocks observed by deep Chandra and lensing observations. Due to the impact of the merger on the mass profiles, previous mass estimates from weak lensing are too high. The plane of the merger is tilted further from the plane of the sky than estimated previously, up to $30^\circ$ from the plane of the sky. We discuss the applicability of our results to multi-wavelength surveys of galaxy clusters.