Me (Thai) and my child's father (Foreigner) have not registered their marriage. But we applied for child certification without using a lawyer. By preparing documents to submit to the court myself.
My husband had the same situation as you last month. And I asked immigration. They said it would be fine if it was a holiday. They grant you. This can be done on the next working day, that is Monday and if you go after Monday it will be considered overstay.