Although the spectrum of primordial fluctuations has been accurately measured on scales
above ∼ 0.1 Mpc, only upper limits exist on smaller scales. In this study, we
investigate generic monochromatic enhancements to the ΛCDM spectrum that trigger the
collapse of ultracompact minihalos (UCMHs) well before standard structure formation. We refine
previous treatments by considering a mixed population of halos with different density profiles,
that should realistically arise as a consequence of late-time accretion and mergers. Assuming that
dark matter (DM) can self-annihilate, we find, as expected, that UCMHs can greatly enhance the
annihilation rate around recombination, significantly imprinting the cosmic microwave background (CMB) anisotropies. However, we provide additional insight on the theoretical uncertainties that
currently impact that boost and which may affect late-time probes such as the 21 cm line or
γ-ray signals. We derive constraints on the primordial power spectrum on small scales using
the ExoCLASS/HYREC codes and the Planck legacy data. We account for the velocity
dependence of the DM annihilation cross-section (s- or p-wave), annihilation channel, the DM
particle mass and the inclusion of late-time halo mergers. Our s-wave constraints are
competitive with previous literature, excluding primordial amplitudes 𝒜*≳
10-6.5 at wavenumbers k ∼ 104 - 107 Mpc-1. For the first time, we highlight
that even p-wave processes have constraining power on the primordial spectrum for cross-sections
still allowed by currently the strongest astrophysical constraints. Finally, we provide an
up-to-date compilation of the most stringent limits on the primordial power spectrum across a wide
range of scales.