Without any orders in place the situation is high risk.
No one can advise you what to do now as the situation is best guided by you and your conscience.
You are right in saying that with no orders in place there is little the Police can do to help.
However the question is also about co-parenting until the child/children involved reach 18 years of age.
If you have an agreement in place and now you dishonor that agreement due to nothing else but your fear then how are you possibly going to co-parent for years to come.
Insofar as the CSA not recognizing him as the father, this does not limit the Family Court from recognising him as the father. 
If you need to remove doubt get a DNA test but even then the Family Court may still recognise him as the father or as having paternal rights to time with the child depending on how many years they have known each other.