Personally, I would go with the manual.
I just got a 40c and just field stripped it for the first time today and I don't recall it saying anything about pulling the trigger during breakdown.
Basically you do the following:
1) Clear the firearm & make sure it is not loaded
2) Drop the mag
3) Pull the slide back & lock it back with the slide lock
4) Push the sear lever downward (using the tool under the grip if so inclined)
5) Hold the slide and rotate the takedown lever all the way downward
6) Carefully slide the slide to the rear a bit until it releases and then slide it forward off of the bottom part of the frame.
That was it in a nutshell. Again, I would go with what S&W states to do in their manual verses what someone on Youtube says to do. But that's just what I would do. S&W designed it, so they should know best on what to do.
Hope this helps,
Mat