Both solar flares and shock waves driven by fast coronal mass ejections (CMEs) can accelerate charged particles in the solar corona and create transient enhancements of solar energetic particle fluxes in interplanetary space (SEP events). Fast CMEs and flares often occur together, which makes it difficult to directly identify the actual source of SEP events detected near Earth orbit. In this paper, we attempt to single out fast CMEs without any signature of particle acceleration related to a flare. We choose meter-wave radio emission from energetic electrons as a tracer of flare-related particle acceleration. In truly radio-silent fast CMEs, the only source of SEP acceleration should be the CME shock. The SOHO LASCO catalog by St. Cyr et al. contains 24 fast CMEs (V > 900 km s-1) located above the western solar limb that occurred between 1996 July and 1998 June. Of these, only three are radio-silent. Comparison of their speeds with the fast magnetosonic speed in the corona shows that these three CMEs very likely drive coronal shock waves. Their properties do not depart significantly from a reference set of SEP-associated fast CMEs, except for their smaller angular width. Although one, possibly two of these three CMEs are accompanied by weak enhancements of the electron and proton fluxes (Ep < 20 MeV; SOHO COSTEP and ACE EPAM), none produces a conspicuous SEP event. This suggests that either CME shocks accelerate particles over much smaller angular ranges than generally believed or that they are less efficient accelerators at energies above ~10 MeV than often thought.