Whilst you're correct in saying it won't fit, your reasoning is flawed - it has nothing to do with the number of camshafts - the reason it won't fit is the motors are two different families and the bore dimensions & spacings are different. The 2.0 is a J series, the 1.6 is G series.
For what it's worth - you can swap the G13 DOHC head onto the G13 SOHC block (the G13 was the only G series motor offered with a DOHC head) - you may need to swap the rotating assembly depending on which version of the motor you're dealing with - as the DOHC is a 16 valve motor, and the SOHC was available with either 8 or 16 valves - you can also swap the heads between the G13, G15 & G16 engines - in fact, the 16v SOHC versions of these three motors all use the same part number.
You can also swap the heads (and the blocks) between the J18 & J20 motors, I believe the head will also fit the J23, but not the J24 - it should be noted here that there are variations amongst the later J series so whilst the heads will bolt up you may find that camshafts and cam sensors are different and so on.