To enable non-destructive quantitative identification of mixed salts in mural plaster layers, hyperspectral data were collected from Na₂SO₄-CaCl₂ mixed-salt samples. Based on these data, a method integrating spectral preprocessing, feature-set construction, and machine-learning inversion was proposed. First, the original spectra were preprocessed using Savitzky-Golay smoothing and multiplicative scatter correction. A 0.6-order fractional-order derivative (FOD) was then introduced to enhance subtle salt-related spectral features. Subsequently, 30 single-band features were selected using a two-step strategy involving competitive adaptive reweighted sampling for preliminary screening and variable importance in projection for secondary screening. On this basis, dual-band and tri-band spectral indices were further constructed, and a combined-band feature set was formed by integrating the three feature sets. Gaussian process regression (GPR) was used to compare the inversion performance of different feature-input strategies for Na₂SO₄ and CaCl₂ contents. The results showed that the 0.6-order FOD achieved a favorable balance between feature enhancement and noise suppression. Among the evaluated feature-input strategies, the combined-band model showed the best predictive performance for both Na₂SO₄ and CaCl₂. These results indicate that integrating complementary information from feature sets with different dimensions can improve the stability and accuracy of mixed-salt inversion, providing a useful reference for the hyperspectral non-destructive quantification of mixed salts in murals.