Bump. I have ruled out it is not Tweetbot, so it is something built into OSX; this might make removing the sound file easier, but I can't find a "swoosh" like sound anywhere. Either Mail, or FB/Twitter at this point.
Leaving Apple some feedback on their page to let us remove Sounds for Twitter/Facebook in Notification Settings, I suggest you do the same if you're curious about this problem.
I had this issue and was wondering what the culprit was a few months ago. Turns out in Messages (or i guess iChat if your running it) has notification sounds set on as default. The swashing sound is caused by a buddy becoming unavailable. This can be disabled by going into Messages > Preferences > Alerts > Event > Buddy Becomes Available/Unavailable, and unchecking the "Play A Sound" option.
Hope this helped.