If you don't mind a solution that's not purely in software, you might try wiring the headphone output to the sound input, and then you just need a way to play a sound from LabVIEW. I've never done this but I suspect it can be done simply (if nothing else, you can use System Exec to launch a separate audio player and specify the filename). I don't know how you would make sure that the call connected prior to playing the sound, you'll have to see if there's some way to determine that from the Skype interface. Also, if your computer doesn't have a "line" input but does have a microphone input, you might have to adjust the volume levels carefully to make it work.
