The dynamic topology of Low Earth Orbit (LEO) mega-constellations is currently posing a significant challenge for handover management because frequent satellite switching can disrupt connectivity and degrade Quality of Service (QoS). Conventional decision-making algorithms also often trigger superfluous handovers. Therefore, this study aims to address the challenges by proposing an Adaptive Hybrid-TOPSIS handover decision strategy that integrates subjective user preferences (Analytic Hierarchy Process) with objective data dispersion weights (Shannon Entropy). The integration of geodesic vector-based analysis allows the hybrid method to dynamically adapt decision criteria to prioritize satellites with geometric continuity to effectively filter out unstable candidates. The simulation conducted using the Starlink Shell-1 constellation model showed that the proposed algorithm significantly outperformed baseline methods. The Hybrid-TOPSIS specifically reduced the average handover frequency by approximately 33% relative to AHP-SAW and 47% to SD-TOPSIS. The increase in stability was achieved without compromising network quality. The proposed method also maintained a negligible Packet Loss Ratio (PLR < 6.5%) and delivered consistent throughput performance comparable to aggressive switching strategies. Furthermore, empirical analysis identified an efficiency boundary by showing that the performance gains of the hybrid framework saturated when the weight dominance of a single attribute exceeded 0.7. The result confirmed that the prioritization of geometric awareness over instantaneous signal peaks was a decisive factor for robust mobility management in next-generation non-terrestrial networks. © 2013 IEEE.