This paper presents an efficient analytical framework for evaluating the performance of inter-satellite communication systems utilizing orbital angular momentum (OAM) beams under pointing errors. An accurate analytical model is first developed to characterize intermodal crosstalk caused by beam misalignment in OAM-based inter-satellite links. Building upon this model, we derive efficient expressions to analyze and optimize system performance in terms of bit error rate (BER). Unlike traditional Monte Carlo-based methods that are computationally intensive, the proposed approach offers accurate performance predictions. This enables a substantial decrease in computation time while maintaining high accuracy, thanks to the use of analytical expressions for both crosstalk and BER. This fast and accurate evaluation capability is particularly critical for dynamic low Earth orbit (LEO) satellite constellations, where network topology and channel conditions change rapidly, requiring real-time link adaptation. Furthermore, we systematically design and evaluate asymmetric OAM mode sets, which significantly outperform symmetric configurations in the presence of pointing errors. Our results also reveal key insights into the interaction between beam divergence, tracking accuracy, and link distance, demonstrating that the proposed framework enables real-time optimization of system parameters with high fidelity. The analytical findings are rigorously validated against extensive Monte Carlo simulations, confirming their practical applicability for high-mobility optical wireless systems such as LEO satellite networks.