Since I'm new to Twitter I just made an ActiveWord for http://search.twitter.com/. Now I type, or ink, "tws" then initiate ActiveWords. A dialog appears (below), enter the search term and my browser launches (if not running) with the results. Simple. Because ActiveWords works everywhere it's not application specific like a browser add-in.
To it set up get ActiveWords (free trial), create a new Scripting ActiveWord, assign whatever ActiveWord code you'd like (mine is tws), then copy/paste this string into the action box:
<"http://search.twitter.com/search?q=<INPUTBOX:Search Twitter>">