Upcoming surveys such as LSST{} and Euclid{} will significantly improve the power of weak lensing as a cosmological probe. To maximise the information that can be extracted from these surveys, it is important to explore novel statistics that complement standard weak lensing statistics such as the shear-shear correlation function and peak counts. In this work, we use a recently proposed weak lensing observable -- weak lensing voids -- to make parameter constraint forecasts for an LSST-like survey. We use the cosmoslics{} $w$CDM simulation suite to measure void statistics as a function of cosmological parameters. The simulation data is used to train a Gaussian process regression emulator that we use to generate likelihood contours and provide parameter constraints from mock observations. We find that the void abundance is more constraining than the tangential shear profiles, though the combination of the two gives additional constraining power. We forecast that without tomographic decomposition, these void statistics can constrain the matter fluctuation amplitude, $S_8$ within 0.3% (68% confidence interval), while offering 1.5, 1.5 and 2.7% precision on the matter density parameter, $Omega_{rm m}$, the reduced Hubble constant, $h$, and the dark energy equation of state parameter, $w_0$, respectively. These results are tighter than the constraints from the shear-shear correlation function with the same observational specifications for $Omega_m$, $S_8$ and $w_0$. The constraints from the WL voids also have complementary parameter degeneracy directions to the shear 2PCF for all combinations of parameters that include $h$, making weak lensing void statistics a promising cosmological probe.
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