Over the last few decades, dielectric core and metallic plasmonic shell (Die@Me) nanoparticles have found a wide variety of applications. The trend to reduce the thickness of the metallic coating requires to account for the influence of the nonlocal dispersion on the spectral response of such nanoparticles. In this paper, we use the discrete sources method and the generalized nonlocal optical response model to describe the nonlocality within the plasmonic metal shell. We found that the variation of the plasmonic shell thickness and the elongation of the nonspherical core-shell particle can enlarge the near-field enhancement and the absorption cross section by an order of magnitude. Besides, we show that the nonlocal dispersion can decrease the field enhancement in the wavelength domain up to 2.5 times with a small blue-shift of about 5 nm.