  First proposed in 2013 by Yagi and Yunes, the quasi-universal \emph{I-Love-Q
relations} consist of a set of relations between the moment of inertia, the
spin-induced quadrupole moment and the electric quadrupolar tidal deformability
of neutron stars which are independent of the Equation of State (EoS) within an
accuracy of $\sim1\%$. In this work, we show that these relations hold for
different Skyrme-based nuclear matter EoS and also for the star-like solutions
of different Einstein-BPS-Skyrme-models, some of which do not even present a
barotropic equation of state. Further, other quasi-universal relations are
analyzed, and together with recent GW observations, we use them to select the
generalized Skyrme model that better reproduces observations. Our results
reaffirm both the universality of the \emph{I-Love-Q} relations and the
suitability of generalized Skyrme models to describe nuclear matter inside
neutron stars.
