A measurement of $CP$-violating observables is performed using the decays $B\pm \to DK\pm$ and $B\pm \to D\pi \pm$, where the $D$ meson is reconstructed in one of the self-conjugate three-body final states $KS\pi +\pi -$ and $KSK+K-$ (commonly denoted $KSh+h-$). The decays are analysed in bins of the $D$-decay phase space, leading to a measurement that is independent of the modelling of the $D$-decay amplitude. The observables are interpreted in terms of the CKM angle $\gamma$. Using a data sample corresponding to an integrated luminosity of $9fb-1$ collected in proton-proton collisions at centre-of-mass energies of $7$, $8$, and $13TeV$ with the LHCb experiment, $\gamma$ is measured to be $(68.7-5.1+5.2)\circ$. The hadronic parameters $rBDK$, $rBD\pi$, $\delta BDK$, and $\delta BD\pi$, which are the ratios and strong-phase differences of the suppressed and favoured $B\pm$ decays, are also reported.