Shadows in hyperspectral images lead to reduced spectral intensity and changes in spectral characteristics, significantly hindering analysis and applications. However, current shadow compensation methods face the issue of nonlinear attenuation at different wavelengths and unnatural transitions at the shadow boundary. To address these challenges, we propose a two-stage shadow compensation method based on multi-exposure fusion and edge fusion. Initially, shadow regions are identified through color space conversion and an adaptive threshold. The first stage utilizes multi-exposure, generating a series of exposure images through adaptive exposure coefficients that reflect spatial shadow intensity variations. Fusion weights for exposure images are determined based on exposure, contrast, and spectral variance. Then, the exposure sequence and fusion weights are constructed as Laplacian pyramids and Gaussian pyramids, respectively, to obtain a weighted fused exposure sequence. In the second stage, the previously identified shadow regions are smoothly reintegrated into the original image using edge fusion based on the p-Laplacian operator. To further validate the effectiveness and spectral fidelity of our method, we introduce a new hyperspectral image dataset. Experimental results on the public dataset and proposed dataset demonstrate that our method surpasses other mainstream shadow compensation methods.