Luminescence arising from -decay of radiotracers has garnered much interest recently as a viable in-vivo imaging technique. The emitted Cerenkov radiation can be directly detected by high sensitivity cameras or used to excite highly efficient fluorescent dyes. Here, we investigate the enhancement of visible and infrared emission driven by -decay of radioisotopes in the presence of a hyperbolic nanocavity. By means of a transfer matrix approach, we obtain quasi-analytic expressions for the fluorescence enhancement factor at the dielectric core of the metalodielectric cavity, reporting a hundred-fold amplification in periodic structures. A particle swarm optimization of the layered shell geometry reveals that up to a ten-thousand-fold enhancement is possible thanks to the hybridization and spectral overlapping of whispering-gallery and localized-plasmon modes. Our findings may find application in nuclear-optical medical imaging, as they provide a strategy for the exploitation of highly energetic gamma rays, Cerenkov luminescence, and visible and near-infrared fluorescence through the same nanotracer.