  Coronal mass ejections (CMEs) on stars other than the Sun have proven very
difficult to detect. One promising pathway lies in the detection of type II
radio bursts. Their appearance and distinctive properties are associated with
the development of an outward propagating CME-driven shock. However, dedicated
radio searches have not been able to identify these transient features in other
stars. Large Alfv\'en speeds and the magnetic suppression of CMEs in active
stars have been proposed to render stellar eruptions "radio-quiet". Employing
3D magnetohydrodynamic simulations, we study here the distribution of the
coronal Alfv\'en speed, focusing on two cases representative of a young
Sun-like star and a mid-activity M-dwarf (Proxima Centauri). These results are
compared with a standard solar simulation and used to characterize the
shock-prone regions in the stellar corona and wind. Furthermore, using a
flux-rope eruption model, we drive realistic CME events within our M-dwarf
simulation. We consider eruptions with different energies to probe the regimes
of weak and partial CME magnetic confinement. While these CMEs are able to
generate shocks in the corona, those are pushed much farther out compared to
their solar counterparts. This drastically reduces the resulting type II radio
burst frequencies down to the ionospheric cutoff, which impedes their detection
with ground-based instrumentation.
