Father of my baby-to-be and I were married at time of conception, but divorced before baby is born. He is "undecided" as to whether or not he will be 1) present at hospital for birth or 2) available to sign birth certificate at hospital

From what I see on Texas AG website (and from general email response I received from same site) it appears that because we were married at time of conception and because baby will be born before time limit set by AG's office as to presumption of paternity - the issue isn't disputing the paternity (or allowing baby to have Father's last name) but what to do if he isn't around to actually sign document at hospital.

Is there paperwork or proof I can bring to hospital to make them put his name on paperwork? Or is this something I'll have to take care of after the fact and by spending (more) money?

Please advise.