Autonomous aerial scanning of target structures is crucial for practical applications, requiring online adaptation to unknown obstacles during flight. Existing methods largely emphasize collision avoidance and efficiency, but overlook occlusion-induced visibility degradation, severely compromising scanning quality. In this study, we propose FC-Vision, an on-the-fly visibility-aware replanning framework that proactively and safely prevents target occlusions while preserving the intended coverage and efficiency of the original plan. Our approach explicitly enforces dense surface-visibility constraints to regularize replanning behavior in real-time via an efficient two-level decomposition: occlusion-free viewpoint repair that maintains coverage with minimal deviation from the nominal scan intent, followed by segment-wise clean-sensing connection in 5-DoF space. A plug-in integration strategy is also presented to seamlessly interface FC-Vision with existing UAV scanning systems without architectural changes. Comprehensive simulation and real-world evaluations show that FC-Vision consistently improves scanning quality under unexpected occluders, delivering a maximum coverage gain of 55.32% and a 73.17% reduction in the occlusion ratio, while achieving real-time performance with a moderate increase in flight time. The source code will be made publicly available.