Since you are already in CH, couldn't you track the dad down and invite him to court for a declaration?
Does Ghana have a law where if a parent abandons the family (in this case a son), they give up their parental rights? Does Switzerland?
Somehow it sounds like you raised your son here. Isn't it easier to ask the court? Someone else already suggested that.
Mixed and blended families headaches. Hypothetically, what would have happened if your current husband wanted to adopt your son? My common sense tells me that you two would have had to produce THAT PAPER the Aussies are asking for - the proof that you have the sole custody of your son.
Good luck, and all the best to your son!