Nanofocusing properties of a tip in the form of a dielectric tapered fiber with metal apertureless coating and dielectric nanocladding can be tuned within a wide spectral range by choice of cladding permittivity. The silica core of diameter decreasing from 2 mum to 5 nm in apex is covered with a silver layer and has a 5 nm dielectric cladding. Internal illumination with a radially polarized Laguerre-Gauss beam guided in fiber is used. In body-of-revolution finite-difference time-domain simulations we find that with an increase of the refractive index of nanocladdings the maximum enhancement occurs for increasingly longer wavelengths.