With unequal variances (where I find that $\frac{S^2_{bigger}}{S^2_{smaller}} \le 1.5$, this would be a moderate difference between variances according to Cohen, 1988) I give a range for d where I divide the difference of the means 1) by the bigger (lower bound for d) and 2) by the smaller (upper bound for d) standard deviation.
I should add that this strategy is purely descriptive and only serves the purpose of helping to interpret the size of the difference that may be there. As far as I know there is no statistical-mathematical argument for this strategy.
(I find it helpful though in cases where it seems plausible from a contextual perspective, say, the difference in well-being between control group and treatment group: even if you absolutely should interpret the differences in variability, one could say, that the relative difference between the means seems quite big, assuming the treatment could be modified in a way that it produces more similar outcomes, but moderate at best considering the seemingly very heterogeneous effects of the treatment.)