I've never done this, but here are some ideas that might help:

1) For a graphical test, use the quantile-quantile plot, as described in this article Modeling the distribution of data? Create a Q-Q plot - The DO Loop

2) Transform your data by the inverse CDF and then test whether the result is uniform.

3) You can use PROC NLMIXED to use MLE as described in this paper for the t-distribution: http://www2.sas.com/proceedings/forum2007/181-2007.pdf

The Cauchy MLE is easy find online.

Of course, if the normal variables are independent, then no need to test, since this is the definition of the Cauchy distribution.

Regarding the question "if this does not fit, what procedure can I use to evaluate which distribution...," I recommend that you look at the SEVERITY procedure in SAS/ETS software. Here is an example: SAS/ETS(R) 13.2 User's Guide

Good luck.