Open-set domain generalization (OSDG) tackles the dual challenge of recognizing unknown classes while simultaneously striving to generalize across unseen domains without using target data during training. In this article, an OSDG framework for hyperspectral image classification is proposed, centered on a new Spectral-Spatial Uncertainty Disentanglement mechanism. It has been designed to address the domain shift influencing both spectral, spatial and combined feature extraction pathways using evidential deep learning, after which the most reliable pathway for each sample is adaptively selected. The proposed framework is further integrated with frequency-domain feature extraction for domain-invariant representation learning, dual-channel residual networks for spectral-spatial feature extraction, and evidential deep learning based uncertainty quantification. Experiments conducted on three cross scene hyperspectral datasets, show that performance comparable to state-of-the-art domain adaptation methods can be achieved despite no access to target data, while high unknown-class rejection and known-class accuracy levels are maintained. The implementation will be available at github.com/amir-khb/UGOSDG upon acceptance.