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.
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