P or N channel MOSFET to disconnect a load
What you show is correct, a p-channel power MOSFET in series with the + output, source to the battery manager, and drain to the load (the LED driver).  The question is, what is the amount of daylight when the solar panel output voltage drops MOSFET's gate voltage to the point where it no longer is fully enhanced and starts to "turn off".  It might be lighter or darker than you want.

Separate from that is the amount of time it takes for the FET to go from fully on to fully off.  during this time it can dissipate significant power and get hot enough to destroy itself.  Consider adding a comparator that snaps the FET from on to off.

An added benefit of the comparator is it makes the on/off daylight level adjustable.