I will discuss (compound) Poisson process approximation for stabilizing statistics of a stationary strongly mixing point process. The main results are formulated in a Wasserstein distance and are based on a general bound on the total variation distance of a stationary point process and its Palm measure. The new findings are applied to minimal angles in the stationary Poisson-Delaunay triangulation. In this example, the asymptotic cluster size distribution is explicit and compound Poisson process approximation is established with an explicit convergence rate. The talk is based on joint work with Nicolas Chenavier.