Few-shot remote-sensing fine-grained ship classification (RS-FGSC) faces two coupled challenges: limited annotated samples and mixed-visibility imaging conditions caused by cloud occlusion. Although CLIP-based prompt learning provides useful transfer priors, conventional single-branch adaptation can encounter an over-correction dilemma: robust compensation applied globally may degrade clear samples, whereas clear-image optimization may fail on occluded samples. We propose CADP (Cloud-Aware Dual-Path Prompt Learning), which decouples clear and occluded processing through learnable routing. CADP contains three components: (1) a cloud detector (CloudDetector) trained with auxiliary cloud-state labels for instance-level routing, (2) a fine-grained adapter (FineGrainedAdapter) that preserves discriminative details for clear samples, and (3) a robust compensation path using occlusion-aware prompting (AOPD) from CARP for occluded samples. To evaluate mixed-visibility scenarios, we construct Mixed-Sky benchmarks by combining clear ship images with SeaCloud-Ship cloud-occluded samples introduced by CARP, using controlled cloud-mixed ratios (25%, 50%, and 75%) and a non-overlapping sampling strategy. Experiments from 1-shot to 16-shot show consistent gains over CoCoOp, CLIP-Adapter, and prior robust prompting methods. CADP achieves 35.49% average accuracy, improving the best-performing baseline in our protocol by +4.81 points (+15.7% relative improvement). Component ablations, routing controls, and attention visualizations indicate that explicit routing reduces negative transfer between clear and occluded samples.