There are a number of options for minimal clinically important difference, some of which would make sense with non-symmetric distributions. See this article for an enumeration: Article Approaches for estimating minimal clinically important diffe...
If you feel obliged to stay with some variant of standardized differences (e.g., involving the SD), you could always invoke Chebyshev's inequality, as that defines limits for any shape distribution (however, the resulting intervals would be larger).