How do I clear Apple's java 6 cache after the 2012-006 update?

Due to some applets that I have to use at work being incompatible with Oracle's Java 7, I have had to re-enable Apple's Java 6 plugin by following the directions here:

http://support.apple.com/kb/HT5559

Java 6 does work for me in all of the browsers on the system. However, I am having some issues with an applet and I suspect that the culprit might be in data left in the cache. Since Java Preferences was removed from Applications -> Utilities, how do I go about removing the cache? I have found /Users/<username>/Library/Caches/Java, but removing this directory didn't solve the issue. Since I don't know if this is really the location that Apple's Java 6 stores its cache, I don't know if removing that directory does anything for clearing the cache.

What is the official way to remove Apple's Java cache now that Apple's Java Preferences is gone? Thanks for any and all help!