Can I use both the Mann-whitney and the KS (kolmogorov smirnov) test on the same dataset

I have two sets of data, one for males and females, and I'm analysing the neuronal spike intervals. I want to see if there's a significant difference in the mean interval between males and females. But I also want to see if there's a significant difference in the distribution of these intervals. One could imagine a scenario in which the mean is not different but the distribution is different. So my question is, is it good practice to use both the Mann-whitney to analyse the means and also KS test for the distributions on the same dataset? Thank you.

Notice that, if you show that the means are different,$$^{\dagger}$$ you've already shown that the distributions are different. Even so, since you planned to do two tests and simply stopped after the first test gave a desirable result, you would have to adjust for two p-values as if you calculated both p-values. If you do the adjustment, then I see no harm in doing both tests.
$$^{\dagger}$$That's not quite what Wilcoxon-Mann-Whitney U shows; it's actually a test of distribution equality that has particularly good properties for looking for mean differences.