Context. In the current multi-messenger astronomy era, it is important that information about joint gravitational wave (GW) and electromagnetic (EM) observations through short gamma-ray bursts (sGRBs) remains easily accessible to each member of the GW-EM community. The possibility for non-experts to execute quick computations of joint GW-sGRB detections should be facilitated. Aims. For this study, we constructed a model for sGRBs and added this to the framework of the previously built Gravitational Wave Universe Toolbox (GWToolbox or Toolbox). We provide expected joint GW-sGRB detection rates for different combinations of GW detectors and high-energy (HE) instruments. Methods. We employed and adapted a generic GRB model to create a computationally low-cost top-hat jet model suitable for the GWToolbox. With the Toolbox, we simulated a population of binary neutron stars (BNSs) observed by a user-specified GW detector such as LIGO, Virgo, the Einstein Telescope (ET), or the Cosmic Explorer (CE). Based on the characteristics of each binary, our model predicts the properties of a resulting sGRB, as well as its detectability for HE detectors such as Fermi/GBM, Swift/BAT, or GECAM. Results. We report predicted joint detection rates for combinations of GW detectors (LIGO and ET) with HE instruments (Fermi/GBM, Swift/BAT, and GECAM). Our findings stress the significance of the impact that ET will have on multi-messenger astronomy. While the LIGO sensitivity is currently the limiting factor regarding the number of joint detections, ET will observe BNSs at such a rate that the vast majority of detected sGRBs will have a GW counterpart observed by ET. These conclusions hold for CE as well. Additionally, since LIGO can only detect BNSs up to a redshift of ∼0.1 where few sGRBs exist, a search for sub-threshold GW signals at higher redshifts using sGRB information from HE detectors has the potential to be very successful and significantly increase the number of joint detections. Equivalently, during the ET era, GW data can assist in finding sub-threshold sGRBs, potentially increasing, for example, the number of joint ET-Fermi/GBM observations by ∼270%. Lastly, we find that our top-hat jet model underestimates the number of joint detections that include an off-axis sGRB. We corrected for this by introducing a second, wider and weaker jet component. We predict that the majority of joint detections during the LIGO/Virgo era will include an off-axis sGRB, making GRB170817A not as unlikely as one would think based on the simplest top-hat jet model. In the ET era, most joint detections will contain an on-axis sGRB.