just wait it out.. i was 13 days overdue and ,y dr finally gave me cytotech to soften my cervix... didnt send me into horrible labor and for this ftm my labor was all of 8 hours!!! Nothing you do will cause you to go into labor even the castor oil. the best thing to do is if you dont get induced just let your body do its thing and your baby will come out. but unless your baby is in distress i wouldnt force anything.
Relax, because full term goes from 37 - 42 weeks. Going beyond the absolutely "week 40" is not a concern, and if your doctor believes there's a need to induce labor, you two can discuss that. For now, gentle walks, rest, good food are all the right ingredients for relaxing the body to know that it can go into labor whenever it's ready.
I'm in the same boat as you except at this point I'll take an induction. I find out today if I will get induced tonight or have to wait until next week. I would try walking bouncing on a yoga ball. I personally wouldn't take caster oil at 40 weeks as you can risk having the baby have a bowl movement before its born. And if your cervix hasn't dialated yet it won't do anything... Good luck! Hope to read your little one is here soon.