We study the effect of perturbations on collisions between conventional solitons from different frequency channels in optical fibers. We calculate the intensity of the collision induced emitted radiation, and the changes in the soliton parameters due to the collision. For this aim we develop a perturbation theory with two small parameters: the parameter characterizing the perturbation, and the reciprocal of the frequency difference between the two solitons. We find that for several types of perturbations, the collision-induced emitted radiation can be described as effectively originating from a fast change (with respect to distance along the fiber) in either the dispersion coefficient, or the nonlinearity coefficient. As a result, soliton propagation in a given channel influenced by many collisions with a quasi random sequence of solitons from all other channels, is similar to soliton propagation in fibers with weak disorder in either the dispersion coefficient, or the nonlinearity coefficient.