As there is nothing like GNOME panel applets in Unity, I would like to ask about some possibility to supercede the "Character Palette", a function that I used a lot for comfortable embedding of special chars.
This is not a direct answer to you question, but an alternative suggestion...
I switched to using the compose key after bringing my (US keyboard) laptops to Sweden I found I had to type "å", "ö" and "ä" a lot, and even using the character applet was too slow.
There is a tutorial to enable the compose key here:
And a list of the default shortcuts here: