The blind fusion of unregistered hyperspectral images (HSIs) and multispectral images (MSIs) has attracted growing attention recently. To address the registration challenge, most existing methods employ spatial transformations on the HSI to achieve alignment with the MSI. However, due to the substantial differences in spatial resolution of the images, the performance of these methods is often unsatisfactory. Moreover, the registration process tends to be time-consuming when dealing with large-sized images in remote sensing. To address these issues, we propose tackling the registration problem from the spectral domain. Initially, a lightweight Spectral Prior Learning (SPL) network is developed to extract spectral features from the HSI and enhance the spectral resolution of the MSI. Following this, the obtained image undergoes spatial downsampling to produce the registered HSI. In this process, subspace representation and cyclic training strategy are employed to improve spectral accuracy of the registered HSI obtained. Next, we propose a blind sparse fusion (BSF) method, which utilizes group sparsity regularization to equivalently promote the low-rankness of the image. This approach not only circumvents the need for rank estimation, but also reduces computational complexity. Then, we employ the Proximal Alternating Optimization (PAO) algorithm to solve the BSF model, and present its convergence analysis. Finally, extensive numerical experiments on simulated and real datasets are conducted to verify the effectiveness of our method in registration and fusion. We also demonstrate its efficacy in enhancing classification performance.