Hyperbolic metamaterials (HMMs) offer extensive possibilities for tailoring light-matter interactions due to their anisotropic permittivity. Hyperbolic nanoantennas exhibit distinct modes: a strongly radiative, electric dipole mode and a non-radiative coupled magnetic dipole–electric quadrupole mode. Here, we study optical HMM nanodisks consisting of a silver-silica multilayer and investigate the potential of these nanostructures to function as efficient, dual-channel optical sensors. By tuning material and structural parameters, we design an easy-to-fabricate HMM nanosensor, which offers high sensitivity of both detectable resonances. The sensing substrates are based on amorphous/random arrays of particles, which play a key role in ensuring spectral separation of the modes and maximizing the sensitivity. To confirm the numerical design, we fabricate an amorphous array of hyperbolic nanodisks composed of ultra-smooth thin silver (on a germanium wetting layer) and silica layers using hole-mask colloidal lithography. Sensitivity measurements yield good qualitative agreement with simulations, proving that hyperbolic nanodisks are promising dual-band refractometric sensors with potential use in bio- or environmental monitoring.