I want to say this was covered once on here a long time ago, but I can't remember exactly when or if it even was. I used to be known as the resident camera guru around here, but I haven't been that active in recent months (I'm here just about everyday, but I don't spend that much time browsing or actively playing with camera code anymore).

I know once upon a time I wanted this, and I still want it. You might try searching the User Contributions forum or one of the scripting forums. There have been massive changes to the forum system over the years, and things get moved around and sometimes posts just disappear, so if there was something here then it may or may not have survived.

Perhaps randomly changing the camera's coordinates within a very small range inside a loop would do it. You'd have to build some internal clamps so the camera position wouldn't go crazy and end up 10 miles from where it started. In other words just move around a fixed point. If the camera can be moved by the player then just save the fixed point where ever the camera ends up once the player stops moving it. It might be a bit trickier whenever the camera is in motion, though.

Oh, and good movie reference would be the newest Rambo. Almost every shot is handheld. It has a very documentary style to it.