  The past year has seen numerous publications underlining the importance of a
space mission to the ice giants in the upcoming decade. Proposed mission plans
involve a $\sim$10 year cruise time to the ice giants. This cruise time can be
utilized to search for low-frequency gravitational waves (GWs) by observing the
Doppler shift caused by them in the Earth-spacecraft radio link. We calculate
the sensitivity of prospective ice giant missions to GWs. Then, adopting a
steady-state black hole binary population, we derive a conservative estimate
for the detection rate of extreme mass ratio inspirals (EMRIs), supermassive-
(SMBH) and stellar mass binary black hole (sBBH) mergers. We link the SMBH
population to the fraction of quasars $f_\rm{bin}$ resulting from galaxy
mergers that pair SMBHs to a binary. For a total of ten 40-day observations
during the cruise of a single spacecraft, $\mathcal{O}(f_\rm{bin})\sim0.5$
detections of SMBH mergers are likely, if Allan deviation of Cassini-era noise
is improved by $\sim 10^2$ in the $10^{-5}-10^{-3}$ Hz range. For EMRIs the
number of detections lies between $\mathcal{O}(0.1) - \mathcal{O}(100)$.
Furthermore, ice giant missions combined with the Laser Interferometer Space
Antenna (LISA) would improve the localisation by an order of magnitude compared
to LISA by itself.
