In this paper, we investigate the validation of Blind Source Separation (BSS) methods applied to interstellar dust hyperspectral data cubes. Since the original source signals are unknown, we cannot measure the separation accuracy by means of classical objective criteria. As a consequence, we here propose a cross-validation of the extracted spectra by applying to the measured data various BSS techniques based on different criteria. We show that, with all these methods, we obtain quite the same (physically relevant) estimated interstellar dust spectra. Moreover, we then derive a spatial structure of the emission of the chemical species, which is not used in the separation step and which is physically relevant.