I'm just talking hypotheticals here... suppose you could claim you had a really contagious little cold and didn't want to come coughing and sneezing. Say you'll come next week and then the next week say someone else in the family is sick. Then say your grandma died. I totally agree that you don't need the pressure when the baby is fine but needs to grow without you being stressed and pushed. And I say that as a Christian. Rahab saved lives when she lied and had her own life saved for it.
If the intent is to protect and serve your baby - who is God's heritage - and family, then I think there's no moral objection to a lie. But you will have to decide what your own limits are.
I think that when most women get near their due date, are so ready to be done being pregnant, they'll gladly take any excuse to be induced. He might be thinking you are one of those women, and is trying to help you out. Tell him no, and not to bring it up again .
Whatever you do, remember it's YOUR body. Don't let him bully you. And congrats on being 39 weeks!
I wouldn't worry about it too much. He offered induction, you said no. Just stand your ground. And maybe delay the next appointment. I wouldn't wait til you miss it then lie, I would call now and say, I can't get in til X day (5 days from when they said or something) and i need to reschedule. Just say serious family commitments or something similar have come up and there is no way you can get in until then. With any luck by the appointment day you will have already gone into labour on your own. Do you usually go late? Are you planning an 'Ooops'?