Record sound clip from Skype and immediately playback for teaching purposes

I teach English online via Skype. I want to be able to record what the student says and then play the clip so we can discuss his pronunciation. I can see how to use Audacity or a Skype-specific program to record, but how can I playback the clip so we both can hear it?

When I try, only I can hear the playback because it’s not being directed to the sound out. Is there software that will do this? Is there a way to use cables between the sound card inputs and outputs to do it? I use a USB headset right now, so I’m not tapping into the input and output connections on the card.

Thanks.