Meta-learning facilitates few-shot hyperspectral target detection (HTD), but adapting deep backbones remains challenging. Full-parameter fine-tuning is inefficient and prone to overfitting, and existing methods largely ignore the frequency-domain structure and spectral band continuity of hyperspectral data, limiting spectral adaptation and cross-domain generalization.To address these challenges, we propose SpecMamba, a parameter-efficient and frequency-aware framework that decouples stable semantic representation from agile spectral adaptation. Specifically, we introduce a Discrete Cosine Transform Mamba Adapter (DCTMA) on top of frozen Transformer representations. By projecting spectral features into the frequency domain via DCT and leveraging Mamba's linear-complexity state-space recursion, DCTMA explicitly captures global spectral dependencies and band continuity while avoiding the redundancy of full fine-tuning. Furthermore, to address prototype drift caused by limited sample sizes, we design a Prior-Guided Tri-Encoder (PGTE) that allows laboratory spectral priors to guide the optimization of the learnable adapter without disrupting the stable semantic feature space. Finally, a Self-Supervised Pseudo-Label Mapping (SSPLM) strategy is developed for test-time adaptation, enabling efficient decision boundary refinement through uncertainty-aware sampling and dual-path consistency constraints. Extensive experiments on multiple public datasets demonstrate that SpecMamba consistently outperforms state-of-the-art methods in detection accuracy and cross-domain generalization.