Which correlation method to us?

I am debating whether to use Pearson’s correlation or Kendall’s tau on a set of data. While linear relationships among subsets of the data are reasonable, I am deeply skeptical that they exist throughout the data, so I am reluctant to use Pearson’s correlation. Also, while I’ve read on Research Gate that Kendall’s tau is preferable to Spearman’s rho for smaller data samples (like mine), I also read that it’s used generally for ordinal data — which brings me back to Pearson’s metric.

Keeping in mind that the results from the "winning" method will be inputted into a copula that will be involved in a week-long simulation, I’d like to get it right the first time, and was hoping your advice could steer me in the right direction.

Thank you!