Unfortunately, there is no good way to remove camera shake--to put it bluntly, the best way to get rid of it is to shoot in a manner that eliminates it in the first place. No judgement, though, I've been in your position before.
You can sometimes get decent results by applying (in the graphics/editing package of your choice; I use Adobe After Effects) a motion tracker to a steady point in the footage, and then applying the output of that motion tracker to the position of the video. This will somewhat stabilize the footage; however, you'll have to crop the footage to the extent that the tracker moves it. So if the footage bounces up by 20 pixels, the tracker will adjust it down by 20 so that the steady point remains in the same place; you'll then have to crop the overall canvas by 20 pixels so that the edge of the video doesn't become visible.
A more comprehensive tutorial on this technique in After Effects
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