Yes, you need to change Skype to use the soundcards that you're using with Breakaway.
If you're using Breakaway to process your voice, then you need the output soundcard of Breakaway to be the input soundcard of Skype.
If you're using Breakaway to process the output of Skype, you need the output soundcard of Skype to be the input soundcard of Breakaway.
The first Input and last Output of the pair should be whatever sources you want… so for input… your microphone. The output should be whatever soundcard you want the sound to come from.