The binary neutron star merger responsible for the gravitational wave event, GW170817, strengthened the merger association with short-duration gamma-ray bursts (SGRBs) following the detection of the SGRB counterpart, GRB 170817A. Here we consider the constraints on a population of local gamma-ray bursts with moderately short duration ($T_{90}<4$ s) and within $d < 200 $ Mpc, that may have originated from similar compact binary mergers. Using well localised gamma-ray bursts from $\sim14.5$ years of Swift/Burst Alert Telescope monitoring, we find no events with high likelihood of being in this distance range, and place an upper limit for the all-sky rate of such events of $<4\ y^{-1}$. For Fermi/Gamma-ray Burst Monitor (GBM) and CGRO/Burst And Transient Source Experiment (BATSE) detected bursts, where the localisation has considerably larger uncertainties, we cross-correlated with 2MASS Redshift Survey galaxies at $d<100$ Mpc, obtaining a weaker constraint of $< 12\ y^{-1}$. A separate correlation search from the GBM and BATSE bursts for giant flares originating from soft gamma-ray repeaters in nearby galaxies ($d < 11 $ Mpc) yields an upper limit of $<3\ y^{-1}$.