In cognitive radio networks (CRNs), dynamic spectrum handoff requires efficient path planning to minimize the overhead of frequent channel switching. This paper proposes a polynomial-time approximation algorithm for spectrum handoff scheduling, based on an improved Traveling Salesman Problem (TSP) modeling of the channel switching sequence. A two-phase cooperative mechanism is designed to minimize frequency-hopping overhead. We rapidly generate diverse candidate channel-switching sequences using a probabilistic method guided by real-time spectrum availability distributions. We dynamically merge locally optimal sub-paths by leveraging historical channel quality data and predicted primary user (PU) behavior in a fuzzy-logic framework. Theoretical analysis shows that the algorithm runs in worst-case O(N^4) time under a dynamic TSP variant, significantly outperforming traditional heuristic methods in scalability. Simulations demonstrate an average deviation of only 0.35% from the optimal solution. In dynamic interference scenarios, the proposed approach reduces spectrum switching delay by 41.2% compared to baseline strategies.Our algorithm effectively resolves distributed spectrum handoff conflicts in multi-user CRN scenarios.