Given the operational disruptions caused by thunderstorms, this paper introduces an innovative approach to flight trajectory optimisation within the context of air traffic management, with a particular focus on minimising disruptions due to adverse weather conditions. The proposed framework integrates wake turbulence separation requirements, node conflict evaluations, and real-time operational constraints to address the complexities inherent in trajectory planning. Unlike previous studies that addressed stochastic optimal control problems for conflict resolution offline, this study presents an enhanced Selective Simulated Annealing (SSA) algorithm for online conflict mitigation. A case study conducted in the approach area of Chengdu Shuangliu International Airport (CTU), involving over 900 flights, demonstrates the applicability and effectiveness of the proposed algorithm. This result underscores the algorithm's potential as a powerful tool for trajectory optimisation, offering significant improvements in operational performance in a timely manner. Additionally, sensitivity analysis of the slot shift ranges confirms the robustness of the selected parameters, highlighting their role in minimising delays and maintaining system efficiency. By deactivating decisions individually, this study also discusses the sensitivity of the algorithm to the proposed decision combinations.