Hyperspectral imaging has the potential to improve intraoperative decision making if tissue characterisation is performed in real-time and with high-resolution. Hyperspectral snapshot mosaic sensors offer a promising approach due to their fast acquisition speed and compact size. However, a demosaicking algorithm is required to fully recover the spatial and spectral information of the snapshot images. Most state-of-the-art demosaicking algorithms require ground-truth training data with paired snapshot and high-resolution hyperspectral images, but such imagery pairs with the exact same scene are physically impossible to acquire in intraoperative settings. In this work, we present a fully unsupervised hyperspectral image demosaicking algorithm which only requires exemplar snapshot images for training purposes.