A search for \CP violation in Cabibbo-suppressed $D^{\pm}\rightarrow
K^0_{\mathrm{S}} K^{\pm}$ and $D^{\pm}_{s}\rightarrow K^0_{\mathrm{S}}
\pi^{\pm}$ decays is performed using $pp$ collision data, corresponding to an
integrated luminosity of 3~fb$^{-1}$, recorded by the LHCb experiment. The
individual $CP$-violating asymmetries are measured to be \begin{eqnarray*}
\mathcal{A}_{CP}^{D^{\pm}\rightarrow K^0_{\mathrm{S}} K^{\pm}} & = & (+0.03
\pm 0.17 \pm 0.14) \%
\mathcal{A}_{CP}^{D^{\pm}_{s}\rightarrow K^0_{\mathrm{S}} \pi^{\pm}} & = &
(+0.38 \pm 0.46 \pm 0.17) \%, \end{eqnarray*} assuming that $CP$ violation in
the Cabibbo-favoured decays is negligible. A combination of the measured
asymmetries for the four decay modes $D^{\pm}_{(s)}\rightarrow K^0_{\mathrm{S}}
K^{\pm}$ and $D^{\pm}_{(s)}\rightarrow K^0_{\mathrm{S}} \pi^{\pm}$ gives the
sum \[
\mathcal{A}_{CP}^{D^{\pm}\rightarrow K^0_{\mathrm{S}} K^{\pm}} +
\mathcal{A}_{CP}^{D^{\pm}_{s}\rightarrow K^0_{\mathrm{S}} \pi^{\pm}} = (+0.41
\pm 0.49 \pm 0.26) \%. \] In all cases, the first uncertainties are statistical
and the second systematic. The results represent the most precise measurements
of these asymmetries to date and show no evidence for CP violation.