Had the exact same question. According to this postthis post and Wilcox (p166) you shouldn't calculate Z and Cohen's D respectively because their calculation is based on the normality assumption.
Wilcox provides robust alternatives to Cohen's D (p166-170) including R code in his book. Got the book from my library. It is also available as e-book in both library networks I have access to.
There are a couple of other posts in this forum asking very similar questions (effect size for WilcoxonWilcoxon, one sample Wilxoconone sample Wilxocon or Mann-Whitney-UMann-Whitney-U tests just to name a few). You might like to look at those too.