Will out of court settlement is acceptable all over the world?
No it is not recognized as per the Indian laws itself where your marriage was solemnised.
Or do I need a court order saying that he is no longer my husband/Spouse.
Yes, you need to dissolve your marriage with her by a decree of divorce by a proper court of law and that will be only authenticated document to prove your status as divorcee.
Will out of court settlement be acceptable all over the world or it is not?
No it cannot be recognised by law of any country.
You better apply for mutual consent divorce by asking him to sign the papers and this divorce case will disposed within 6 months from the date of divorce application.