Avid Xpress (which I purchased, and failed to work out how to use! Or rather, I could not import any of my mpeg data into it.) has a stabiliser tool that can make shaky videos look as if they were taken on a steadicam, perhaps. That is one of the reasons why I purchased Avid. On their site they have footage of a surfer being filmed by another person in the water and making the shaking video of the surfer appear as if it were taken from a tripod rather than a swimmer.
Is there any stabilizer function inside Vegas?