I have no special knowledge of the rates.
However a quick Google search found this:
http://www.cheapestdestinationsblog.com/2013/07/19/how-much-does-it-cost-to-go-through-the-panama-canal/
It’s definitely best to go small than to look like a new money Russian tycoon. Small ships of less than 50 feet in length pay $800 for the transit.
You do not look like a Russian tycoon.
I am definitely not. It's quite alright, it says ~1k for a small yacht. having in mind time you save on around trip around South Americas :) Corinth even though savings in time was much smaller was about ~100EUR i believe. And if you can spare a day or two going around, that would be totally different story doing a roundabout of a few weeks.