I am using the function 'tost' from the package 'equivalence' to conduct a test of equivalence for normally distributed data. In case of non-normally distributed data, I want to conduct the non-parametric equivalent to TOST. I know how to conduct the TOST by myself using two one-sided t-test and take the higher p-value as TOST p-value. Can I simply to the same with the wilcox.test, meaning conducting two one-sided tests against the chosen margins and that's it?
Yes, the confidence interval inclusion principle (decide in favor of equivalence if the confidence interval for your distance measure is completely contained within the equivalence interaval) can also be used with non-parametric tests as e.g. the Wilcoxon sign test. I recommend the book "Testing Statistical Hypotheses of Equivalence and Noninferiority" from Wellek, there you will find a more powerful non-parametric approach (the Mann-Whitney test for equivalence for the two-sample setting). But presumably, this test is not yet implemented in R.