Hey there, sorry for the late reply, i was thinking about this, and looked around for how to code for video capture, but its crazy complicated.
I would suggest setting your camera speed and damping really low to get that nice steady cam feel, and then use something like shadowplay if you have an nvidia card, which i use for all captures and video editing, or FRAPS or OBS.
It would be muuuch easier to use something that has been created for this task than wait for me to do this :)