Is it possible to use the character map as a standalone app?
In this http://hints.macworld.com/article.php?story=20051022020253863 Article, you find the AppleScripts to do what you want. However, the paths seem to have changed at least under Lion. So, to show the Character Palette under 10.7 (possibly older as well), use this AppleScript:

tell application "Finder"
    open item "System:Library:Input Methods:CharacterPalette.app" of the
    startup disk
end tell


As a bonus, the Keyboard Viewer is displayed with this script:

tell application "Finder"
    open item "System:Library:Input Methods:KeyboardViewer.app" of the
    startup disk
end tell


To create a "Standalone Application" from them, just paste them into the AppleScript Editor, choose File->Save As... and select Application as the type.