To test the significance of the skewness difference between two distributions with $N_1$ and $N_2$ samples, would the following test work:
Create a single array of all the samples from both distributions.
Randomly shuffle the array .
Split the array at index $N_1$.
Calculate the $abs()$ of difference of the skewness/kurtosis statistics for the two partitions.
Repeat until desired precision/out of unique permutations.
Then check if the actual $abs()$ difference of skewness/kurtosis statistics lie beyond the $p = 0.05$ interval.