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The James Webb Space Telescope (JWST) will revolutionise our understanding of early galaxy formation, and could potentially set stringent constraints on the nature of dark matter. We use a semi-empirical model of galaxy formation to investigate the extent to which uncertainties in the implementation of baryonic physics may be degenerate with the predictions of two different models of dark matter -- Cold Dark Matter (CDM) and a 7 keV sterile neutrino, which behaves as Warm Dark Matter (WDM). Our models are calibrated to the observed UV luminosity function at $z=4$ using two separate dust attenuation prescriptions, which manifest as high and low star formation efficiency in low mass haloes. We find that while at fixed star formation efficiency, $\varepsilon$, there are marked differences in the abundance of faint galaxies in the two dark matter models at high-$z$, these differences are mimicked easily by varying $\varepsilon$ in the same dark matter model. We find that a high $\varepsilon$ WDM and a low $\varepsilon$ CDM model -- which provide equally good fits to the $z=4$ UV luminosity function -- exhibit nearly identical evolution in the cosmic stellar mass and star formation rate densities. We show that differences in the star formation rate at fixed stellar mass are larger for variations in $\varepsilon$ in a given dark matter model than they are between dark matter models; however, the scatter in star formation rates is larger between the two models than they are when varying $\varepsilon$. Our results suggest that JWST will likely be more informative in constraining baryonic processes operating in high-$z$ galaxies than it will be in constraining the nature of dark matter.