Do NOT fall for that. If he's willing to pay, what's the difference between paying through the state or paying you directly?
Also, I can tell from your question that you need an attorney ASAP! If you not at least consult with a local family law attorney, you are going to deeply regret the outcome of this case and you will regret it for many, many years. I'm not trying to scare you to drum up business for my brethern in Beaumont--it's absolutely clear from your question that you are sucestible to bad ideas from your husband and you need someone to help guide you away from those.
It is in your interest and you child or children's interest to have child support provisions in the court's order. I am winding most of my law practice in Houston and have started a law firm with two other lawyers in Beaumont. I will be in district court in Beaumont for Judge Shelton's final hearings today (Thursday 5/19). If you want to talk about the matter at no cost you can call me. If you are set for one of said hearing call a lawyer early. If not me, someone.
I was a Child Support Enforcement Officer for the Texas Attorney General prior to becoming a lawyer. You can get this done the right way now. Doing it now is easy. It is unlikely a better time will come. This is something you don't need until you need it. Like I said, no cost just a little help. The 279th District Court. Good luck to you and your family.