Autonomous 3D exploration with UAVs requires efficient target selection under limited flight time and onboard computation. In conventional Euclidean-distance-based frontier pipelines, geometric distance may poorly represent the actual collision-free travel cost in cluttered environments, leading to inefficient frontier choices. This paper presents a lightweight path-aware frontier re-ranking method for LiDAR-based UAV exploration. The method first retains a small top-N set of promising frontier candidates using a lightweight utility function and then applies time-bounded RRT* planning to estimate their feasible path costs for re-ranking. The path generated for the selected frontier is further reused for navigation to reduce redundant global planning. Experiments in three warehouse-like environments show that the proposed method consistently produces shorter exploration trajectories than conventional frontier baselines, with traveled-distance reductions of up to 14.1%, while reducing exploration time by up to 9.5% in two environments and remaining competitive in the third. The method maintains map detail comparable to the conventional OctoMap-based baseline, demonstrating an effective trade-off between exploration efficiency and mapping quality.

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