  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.
