Why where is no Process Capability button? Or you can't do it with Cauchy's distribution data.
Have you tried fitting all the Distributions, and then determine which have a significant Goodness Of Fit? You could then use that distribution for your Cp and Cpk
Actually, the mean of the Cauchy distribution is defined but not the higher moments. So, no variance, no standard deviation. No standard deviation, no Ppk.
And, just as an aside, if you're responsible for improving a process that outputs data that are really Cauchy distributed, you might want to update your resume...