Accurate 3D point cloud registration underpins reliable image-guided colonoscopy, directly affecting lesion localization, margin assessment, and navigation safety. However, biological tissue exhibits repetitive textures and locally homogeneous geometry that cause feature degeneracy, while substantial domain shifts between pre-operative anatomy and intra-operative observations further degrade alignment stability. To address these clinically critical challenges, we introduce a novel 3D registration method tailored for endoscopic navigation and a high-quality, clinically grounded dataset to support rigorous and reproducible benchmarking. We introduce C3VD-Raycasting-10k, a large-scale benchmark dataset with 10,014 geometrically aligned point cloud pairs derived from clinical CT data. We propose MambaNetLK, a novel correspondence-free registration framework, which enhances the PointNetLK architecture by integrating a Mamba State Space Model (SSM) as a cross-modal feature extractor. As a result, the proposed framework efficiently captures long-range dependencies with linear-time complexity. The alignment is achieved iteratively using the Lucas-Kanade algorithm. On the clinical dataset, C3VD-Raycasting-10k, MambaNetLK achieves the best performance compared with the state-of-the-art methods, reducing median rotation error by 56.04% and RMSE translation error by 26.19% over the second-best method. The model also demonstrates strong generalization on ModelNet40 and superior robustness to initial pose perturbations. MambaNetLK provides a robust foundation for 3D registration in surgical navigation. The combination of a globally expressive SSM-based feature extractor and a large-scale clinical dataset enables more accurate and reliable guidance systems in minimally invasive procedures like colonoscopy.