A perturbative distorted-wave theory is presented here for evaluating weak-field two-photon spectra, collision-induced energy redistribution, and radiative escape rates, produced by radiatively damped optical collisions of atoms in ultracold atom traps. This theory complements and corroborates a complex-potential theory developed recently. Illustrations are given of the use of the present theory in producing various features of one-color or two-color photoassociation spectra, such as the excited-level bound-state resonance structure, or Condon diffraction in the continuum of the final level.