After some hours of digging, I ran across a suggestion that didn't quite work, but still allowed me to achieve what I was after with a hint of modification. Sharing it here so anyone else who wonders the same thing will have a workaround.
Since there is no differentiation in Skype between sound devices when using Pulse Audio, the simple trick is that you can use a script to call some other applet/application which you can then isolate in the PA Volume Control manager.
Because I have ALSA installed, I also have alsa-utils which comes with a CLI audio player: "aplay". (There may be any number of other suitable apps.)
To convert the Skype behavior:
1) Open the Pulse Audio Volume Control applet and make sure that the
Playback tab is selected; then open
Skype > Options > Notifications > Advanced View.
2) Check "Execute the following script" and type the name of your preferred player, the path to the Skype sounds -- /usr/share/skype/sounds -- and the name of the audio file which is specified a few lines above on the "Play Sound File" line.
I started with the first event -- Skype Login -- because it's a long sound effect.
The script line looks like this:
Code:
aplay /usr/share/skype/sounds/SkypeLogin.wav
3) Uncheck "Play Sound File".
4) Click "Test Event" and jump over to the Pulse Audio Volume Control applet. You should see aplay appear, and there should be enough time to select the stream switcher and change from your headset device to speaker output.
5) Once you've confirmed that it works, you can go through the list of Skype notifications and change every thing that plays a sound file to play using the external, isolated in PA audio player. (There aren't that many of them.)