In the present work, we investigate the thermal conductivity (kappa) of different core-shell nanowires using molecular dynamics simulation and Green-Kubo (EMD), imposing a temperature gradient (NEMD) and M & uuml;ller-Plathe (rNEMD) approaches. We show that in GaAs@InAs nanowires, the interface effect becomes more significant than the nanowire cross-sectional geometry. In particular, kappa decreases as the interface area increases, reaching a minimum, and then increases when the interface strain relaxes. This is particularly important for thermoelectric applications, where minimization of kappa is desired. In particular, the different methods can predict minima at different core diameters without special considerations. In addition, the NEMD approach and, to a lesser extent, rNEMD tend to overestimate the kappa values, which cannot be corrected with the methods available in the literature. By analyzing the temperature and length dependence, (I) we show that interfacial scattering primarily involves phonon-phonon interactions, which mainly affect low-energy modes, a mechanism that effectively reduces kappa at low temperatures. (II) The Langevin thermostat tends to pump low-energy modes in the NEMD approach, but this effect decreases with longer nanowires. (III) Energy exchanges in rNEMD stimulate high-energy phonons, derived from the saturation of kappa at a much shorter nanowire length than NEMD. These findings highlight the challenges of accurately determining kappa of ultrathin core-shell nanowires, where only the EMD approach provides precise results. With the recognition of non-equilibrium contributions to the overestimation of kappa by NEMD and rNEMD, these methods can still provide valuable insights for a comprehensive understanding of the underlying thermal transport mechanisms. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).