I would not cut the video cable to separate them. But it looks like  great buy for less than $2. The Apple cable is great but not at 5 - 10X the price of the regular cable.

If the line is coming from the monitor alone looks like either a shield is missing inside or bad caps/broken solder joints on the board. You can go in and desolder the bad looking joints and then resolder them. Look for burnt connectors and swollen caps inside the board.

The third party power supply has me worried, as it could be sending in stray signals. Better to get an Apple IIc power pack or a Laser 128/Laser XT power pac. The Laser power pac is more beefier than the Apple one.