I would use the 20cm zip and just increase the length of the jacket to accommodate it. Adding 2cm to the length will be negligible, even on a child’s jacket.
I’ve shortened an open ended zip, but done it from the top, as you need the bottom ends to slot together, so I shortened from the top, by removing the teeth and folded the cut end inside the the neck. You just end up with a longer piece of zip without teeth, so just cut off to 5/8th” or 1.5cm.