There are no predefined methods in scripts for selecting unused character styles. This may annoy you. If you just wanted to delete without confirmation, I would suggest running the action from a script with alerts disabled. But since your action is just one part of a chain of other actions, this option does not seem to suit you. The following code is of little use under your task conditions.
#target illustrator
app.userInteractionLevel = UserInteractionLevel.DONTDISPLAYALERTS;
app.doScript("ActionName","SetName");
app.userInteractionLevel = UserInteractionLevel.DISPLAYALERTS;