Dynamic triggering of large, detectable slow slip events (SSEs) is rarely observed, even though regional earthquakes often trigger tectonic tremors and very low frequency earthquakes. In this study, we investigate stress sensitivity of dynamic triggering of shallow SSEs in the Nankai Trough offshore of Kii Peninsula, Japan. We first identify additional shallow SSEs that have not been reported in previous studies and obtain a 15-year-long catalog of SSEs, some of which are triggered by passing seismic waves originating from large regional earthquakes. We then quantify dynamic and static stress perturbations on the plate interface induced by 19 candidate regional earthquakes using numerical simulations of seismic wave propagation. We find that SSE propensity to dynamic triggering depends mainly on the maximum Coulomb stress change and that relatively large dynamic stresses (>10-20 kPa) are needed to trigger a shallow SSE in the Nankai Trough. Regional earthquakes that can induce such large amplitude of dynamic stresses on the plate interface are relatively rare, which might explain the scarcity of dynamic triggering of large, detectable SSEs along the Nankai as well as other subduction zones. In addition, our analysis suggests that intraslab earthquakes can efficiently trigger SSEs in subduction zones via less-attenuated, slab-guided waves. Moreover, our results support the idea that an accretionary wedge in subduction zones promotes the dynamic triggering of shallow SSEs.