I gave Songbird Portable a try.
Once you get past all the configuration screens, it goes to the main Songbird UI.
It immediately loads a webpage that no longer exists, and instead shows a parking page with a bunch of advertisements. Without doing an in-depth analysis of the page, I can say pages like these often contain security and/or privacy issues.
Clicking on the Songbird.me service within the app (left column, about half way down), loads another page that randomly goes to different advertisement pages. Again, it is possible that this poses security and/or privacy issues.
It appears the browser within Songbird is based on the Gecko (Mozilla) engine, and is likely an old version with many unpatched security holes.
Once the user closes Songbird, and reopens it, the initial page no longer loads. If the user does not click on the Songbird.me service, it may not pose an issue.
If possible, the loading of that initial web page within Songbird should be prevented, and the Songbird.me service should be removed.
Security and privacy evaluations also need to be performed.
After writing the above post, I got curious and did a little research.
Here's what I learned (and may already be documented on this site somewhere).
Songbird was discontinued years ago. Source: https://wikipedia.org/wiki/Songbird_%28software%29
Nightingale is the free replacement. Source: https://wikipedia.org/wiki/Nightingale_%28software%29
Nightingale is open-source, available on GitHub: https://github.com/nightingale-media-player
Nightingale has its own website: http://getnightingale.com/
Perhaps Songbird can be removed, and Nightingale added to PortableApps?
Songbird left some files behind in AppData.