I personally feel this as a most confusing question. As per my understanding, if sample size is > 30, and sample is skewed, we can still use paramteric approach, as it will follow Z distribution based on central limit theoram. However, I am seeing many statisticians are suggesting to use non-paramteric approach if data is not normally distributed.
If data is not normally distributed, then I think non-parametric would be the best option.
Nonparametic tests are more exact. In this case, you can use one-way Anova and t in addition to Kruskal Wallis and Mann Whitney.
Since your sample could be large enough, and according to the Central Limit Theorem, you can use t test to compare the means of two groups—albeit lack of normality. You might find the following a good read.
Kwak, S. G., & Kim, J. H. (2017). Central limit theorem: The cornerstone of modern statistics. Korean Journal of Anesthesiology, 70(2), 144. https://doi.org/10.4097/kjae.2017.70.2.144
Good luck,
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