We propose the Lightweight Multimodal Contrastive Attention Transformer (L-MCAT), a novel transformer-based framework for label-efficient remote sensing image classification using unpaired multimodal satellite data. L-MCAT introduces two core innovations: (1) Modality-Spectral Adapters (MSA) that compress high-dimensional sensor inputs into a unified embedding space, and (2) Unpaired Multimodal Attention Alignment (U-MAA), a contrastive self-supervised mechanism integrated into the attention layers to align heterogeneous modalities without pixel-level correspondence or labels. L-MCAT achieves 95.4% overall accuracy on the SEN12MS dataset using only 20 labels per class, outperforming state-of-the-art baselines while using 47x fewer parameters and 23x fewer FLOPs than MCTrans. It maintains over 92% accuracy even under 50% spatial misalignment, demonstrating robustness for real-world deployment. The model trains end-to-end in under 5 hours on a single consumer GPU.