I want to redirect the audio coming from Skype (and only Skype, not other programs running at the same time) over the network. Is there any way to do that?
This can be done quite easily with pulseaudio the default sound server in ubuntu, first make sure that both machines have these packages installed as well as pulseaudio itself of ourse (if the other machine isn't ubuntu it might need installing). These will make the configuation easier.
Next run padevchooser from a terminal or Applications > Sound & Video > PulseAudio Device Chooser
This will load a small application to your system tray area near your clock which enables you to quickly configure and control pulseaudio. The first thing you need to do is configure the machine you was to recieve sound to advertise it's devices over the network then the sending device needs to be configured to add discoaverabe devices to the local sound server.
With that done and the remote devices showing up on the sending machine first use the device chooser icon to open the volume control from the menu. Next start skype and have it begin playing audio, starting the Skype Test Call will work for this when it does you will see skype appear in the list on the playback tab. Next to it above the meter bars on the right will be a drop down box showing the device selected for the audio to be played here you can select the remote vevice you would like the sound to be sent to.