Using Mighty Mouse (requires 10.4.2), you can set any of the actions to open a file, script, application, etc. So I set about making the squeeze action hide the frontmost application.
The AppleScript for this is fairly simple (though, like any AppleScript, I needed to start from similar code online).
tell application "System Events"
set app_name to name of the second process whose frontmost is true
set visible of process app_name to false
end tell
(In case you're curious, the reason why I use the second process is because that when the script is running, the first process is the script itself.)
Mac OS X Hints
http://hints.macworld.com/article.php?story=20060110152311698