The study of cultural heritage (CH) objects benefits greatly from non-invasive techniques like hyperspectral imaging (HSI), which enables material identification and spatial mapping. Due to the heterogeneous composition of CH artifacts, combining complementary techniques is essential for comprehensive analysis. However, handling such high-dimensional datasets remains a challenge. We present a computational protocol that combines spatial and spectral dimensionality reduction to enable early-stage fusion and efficient analysis of fused data, through multivariate methods, with a focus on Uniform Manifold Approximation and Projection (UMAP). We introduce an open-source plugin for Napari viewer, which allows for UMAP-based exploration of fused multimodal datasets. Our approach is demonstrated in case studies involving reflectance and photoluminescence data fusion, showcasing its effectiveness in detecting degradation phenomena and revealing material complexity in both plastic artifacts and historical paintings.