In the companion paper [Phys. Rev. D 103, 104010 (2021)] we have derived the short-ranged potentials for the Teukolsky equations for massless spins (0, $1/2$, 1, 2) in general spherically symmetric and static metrics. Here we apply these results to numerically compute the Hawking radiation spectra of such particles emitted by black holes (BHs) in three different ansatz: charged BHs, higher-dimensional BHs, and polymerized BHs arising from models of quantum gravity. In order to ensure the robustness of our numerical procedure, we show that it agrees with newly derived analytic formulas for the cross sections in the high and low energy limits. We show how the short-ranged potentials and precise Hawking radiation rates can be used inside the code blackhawk to predict future primordial BH evaporation signals for a very wide class of BH solutions, including the promising regular BH solutions derived from loop quantum gravity. In particular, we derive the first Hawking radiation constraints on polymerized BHs from AMEGO. We prove that the mass window $10^{16}–10^{18}\mathrm{g}$ for all dark matter into primordial BHs can be reopened with high values of the polymerization parameter, which encodes the typical scale and strength of quantum gravity corrections.