Heterostructures based on Prussian blue analogues (PBA) combining photo- and magneto-striction have shown a large potential for the development of light-induced magnetization switching. However, studies of the microscopic parameters that control the transfer of the mechanical stresses across the interface and their propagation in the magnetic material are still too scarce to efficiently improve the elastic coupling. Here, this coupling strength is tentatively controlled by strain engineering in heteroepitaxial PBA core-shell heterostructures involving the same Rb0.5Co[Fe(CN)6]0.8·zH2O photostrictive core and isostructural shells of similar thickness and variable mismatch with the core lattice. The shell deformation and the optical electron transfer at the origin of photostriction are monitored by combined in situ and real time synchrotron X-ray powder diffraction and X-ray absorption spectroscopy under visible light irradiation. These experiments show that rather large strains, up to +0.9%, are developed within the shell in response to the tensile stresses associated with the expansion of the core lattice upon illumination. The shell behavior is, however, complex, with contributions in dilatation, in compression or unchanged. We show that a tailored photo-response in terms of strain amplitude and kinetics with potential applications for a magnetic manipulation using light requires a trade-off between the quality of the interface (which needs a small lattice mismatch i.e. a small a-cubic parameter for the shell) and the shell rigidity (decreased for a large a-parameter). A shell with a high compressibility that is further increased by the presence of misfit dislocations will show a decrease in its mechanical retroaction on the photo-switching properties of the core particles.