Visual navigation is a core capability for mobile robots, yet end-to-end learning-based methods often struggle with generalization and safety in unseen, cluttered, or narrow environments. These limitations are especially pronounced in dense indoor settings, where collisions are likely and end-to-end models frequently fail. To address this, we propose SaferPath, a hierarchical visual navigation framework that leverages learned guidance from existing end-to-end models and refines it through a safety-constrained optimization-control module. SaferPath transforms visual observations into a traversable-area map and refines guidance trajectories using Model Predictive Stein Variational Evolution Strategy (MP-SVES), efficiently generating safe trajectories in only a few iterations. The refined trajectories are tracked by an MPC controller, ensuring robust navigation in complex environments. Extensive experiments in scenarios with unseen obstacles, dense unstructured spaces, and narrow corridors demonstrate that SaferPath consistently improves success rates and reduces collisions, outperforming representative baselines such as ViNT and NoMaD, and enabling safe navigation in challenging real-world settings.