We consider a cache-aided wireless device-to-device (D2D) network of the type introduced by Ji et al., where the placement phase is orchestrated by a central server. We assume that the devices' caches are filled with uncoded data, and the whole content database is contained in the collection of caches. After the cache placement phase, the files requested by the users are serviced by inter-device multicast communication. For such a system setting, we provide the exact characterization of the optimal load-memory trade-off under the assumptions of uncoded placement and one-shot delivery. In particular, we derive both the minimum average (under uniformly distributed demands) and the minimum worst-case sum-load of the D2D transmissions, for given individual cache memory size at disposal of each user. Furthermore, we show that the performance of the proposed scheme is within factor 4 of the information-theoretic optimum. Capitalizing on the one-shot delivery property, we also propose an extension of the presented scheme that provides robustness against random user inactivity.