Recent theoretical considerations and observational evidence evince the spine-sheath morphology of relativistic jets emitted from active galactic nuclei (AGNs) or gamma-ray bursts (GRBs). The resulting shear boundary layers (SBLs) are likely to be an avenue for particle acceleration in relativistic jets. The effect of radiation drag on radiating particles has yet to be addressed in most studies of particle acceleration at shear boundary layers, even though radiative cooling may considerably affect particle dynamics. By using particle-in-cell simulations, we study the effects of inverse Compton cooling on particle dynamics and emerging particle spectra.