Nothing in a UV formulation cures without a photoinitiator. It is the component that converts light into chemistry, absorbing photons at a specific wavelength and breaking apart into free radicals that initiate the acrylate polymerisation.
Photoinitiator selection is wavelength matching. Each photoinitiator has an absorption spectrum, and it has to overlap with the output of your lamp. This is why switching from a mercury lamp to LED UV is not a lamp swap — LED output is narrow-band (commonly 365, 385 or 395 nm) and most conventional photoinitiators absorb poorly there. The formulation has to change.
Pigmentation complicates it further: pigment competes for the same photons. White and black systems need substantially more photoinitiator, or more energy, than a clear coat at the same film thickness.