Abstract We introduce a publicly available full-sky beam convolution code library intended to inform the design of future cosmic microwave background instruments and help current experiments probe potential systematic effects. The code can be used to assess the impact of optical systematics on all stages of data reduction for a realistic experiment, including analyses beyond power spectrum estimation, by generating signal timelines that may serve as input to full analysis pipelines. The design and mathematical framework of the python code is discussed along with a few simple benchmarking results. We present a simple two-lens refracting telescope design and use it together with the code to simulate a year-long data set for 400 detectors scanning the sky on a satellite instrument. The simulation results identify a number of sub-leading optical non-idealities and demonstrate significant B-mode residuals caused by extended sidelobes that are sensitive to polarized radiation from the Galaxy. For the proposed design and satellite scanning strategy, we show that a full physical optics beam model generates B-mode systematics that differ significantly from the simpler elliptical Gaussian model.