We investigate the asymmetry of shadows of rotating black holes, as a source of information on their interior content, for black holes of the Kerr-Schild class, specified by T^t_t = T^r_r. Non-singular black holes of the Kerr-Schild class, satisfying the weak energy condition, are described by de Sitter-Kerr solutions, asymptotically de Sitter as r → 0. We obtain the direct relation between the mass function for a de Sitter-Kerr black hole, and the celestial coordinates of its shadow, as well as the direct relation of the interior density for an extreme black hole with the celestial coordinates of its double horizon, which presents the boundary of its shadow. Application of these relations for analysis of an observed black hole shadow would allow to get information on its interior content, and to consider the presence or absence+ of a singularity in its deep interior.