Swizzle is a data access pattern optimization technique by reorganizing the execution order of computational tasks to improve the cache locality in modern NPUs. Existing analysis and optimization techniques lack support for swizzle-aware modeling on NPUs and fail to effectively capture cache behavior across diverse swizzle configurations. To this end, we propose SnakeMan, a framework for modeling and optimizing swizzle. We introduce a relation-centric notation to characterize different cache access patterns, thus exploring wider swizzle space. Then, we propose a hybrid performance model based on set theory for cache analysis. The proposed performance model uses an analytical approach to quantify cache miss behavior under unsaturated cache conditions (\textit{non-saturated misses}), and employs a simulation method combined with an early exiting mechanism to model cache behavior under saturated cache conditions (\textit{saturated misses}). Experimental evaluations demonstrate that SnakeMan achieves an average modeling accuracy of 93.5% in transfer latency compared to real-world hardware. Evaluation on a variety of DNNs shows that SnakeMan outperforms existing tensor program optimizers by up to 1.5$\times$ on A100 GPUs. We also demonstrate NPU cache size optimization based on SnakeMan.