Hi,
So first, custom address fields are displayed in several places. So you'll have to edit the file "custom_fields" (or custom_fields_bootstrap if the use bootstrap design setting is activated on your HikaShop configuration) of the view "user" for the registration form. And the file "form" of the view "address" for the address edition form.
There, you want to change the line:
' '.$onWhat.'="hikashopToggleFields(this.value,\''.$fieldName.'\',\''.$type.'\',0);"',
which handles the toggling of the fields when a field is changed.
I would recommend to add there a call to a custom javascript function with this.value and only add that call if the field is the post code field (you can check $fieldName for that).
Then, to your own check in your javascript function and hide/display the line you want with a getElementById on the id of the row in the DOM.