Very difficult to do with the existing cache code. It's a journaled on-disk datastructure that is not designed to support privacy, and privacy is not a feature you can add on top.
One option is to mount an encrypted disk image and put the cache in there. Similar to Mac OS X's FileVault for example. If you can figure out how to do that, you're golden.
Your other option is to implement your own cache, using the existing cache as a guide. Fair warning: the OkResponseCache is subject to change in the next release!