Hyperspectral imaging (HSI) captures detailed spectral signatures across hundreds of contiguous bands per pixel, being indispensable for remote sensing applications such as land-cover classification, change detection, and environmental monitoring. Due to the high dimensionality of HSI data and the slow rate of data transfer in satellite-based systems, compact and efficient models are required to support onboard processing and minimize the transmission of redundant or low-value data. To this end, we introduce a novel curriculum multi-task self-supervised learning (CMTSSL) framework designed for lightweight architectures for HSI analysis. CMTSSL integrates masked image modeling with decoupled spatial and spectral jigsaw puzzle solving, guided by a curriculum learning strategy that progressively increases data difficulty during self-supervision. This enables the encoder to jointly capture fine-grained spectral continuity, spatial structure, and global semantic features. Unlike prior dual-task SSL methods, CMTSSL simultaneously addresses spatial and spectral reasoning within a unified and computationally efficient design, being particularly suitable for training lightweight models for onboard satellite deployment. We validate our approach on four public benchmark datasets, demonstrating consistent gains in downstream segmentation tasks, using architectures that are over 16,000x lighter than some state-of-the-art models. These results highlight the potential of CMTSSL in generalizable representation learning with lightweight architectures for real-world HSI applications. Our code is publicly available at https://github.com/hugocarlesso/CMTSSL.