We investigate chemical and thermal freeze-out time dependencies for strange particle production for CERN SPS heavy ion collisions in the framework of a dynamical hadronic transport code. We show that the Lambda yield changes considerably after hadronization in the case of Pb+Pb collisions, whereas for smaller system sizes (e.g. S+S) the direct particle production dominates over production from inelastic rescattering. Chemical freeze-out times for strange baryons in Pb+Pb are smaller than for non-strange baryons, but they are still sufficiently long for hadronic rescattering to contribute significantly to the final Lambda yield. Based on inelastic and elastic cross section estimates we expect the trend of shorter freeze-out times (chemical and kinetic), and thus less particle production after hadronization, to continue for multi-strange baryons.