For the airlines that have policies in place, they work on an honor system. It is illegal for them to ask you how far along you are, or even if you are pregnant. Under the Americans With Disabilities Act, they cannot ask about medical conditions. It is up to you as the individual to ask the business for any special services you might need and they have to cooperate tothe best of their ability.
As a pregnant person, you don't have to ask for any special services besides not sitting in an emergency exit row, so I wouldn't even mention it. If you have no risk factors for preterm labor I say go and enjoy it.
FWIW, I was evacuated from my home at 35 weeks and flew 10 hours to get to safety. I had no issues, save for being uncomfortable sitting for so long.