confused and need opinions

I'm a FTM and this Friday I will be 38 weeks. Still not dilated and not effacing what so ever. My OB who I have seen since I was 15 (due to medical reasons) is leaving the week of the babies due date, and I don't feel comfortable with another person delivering my baby.. He gave me the option of being induced at 39 weeks, but he doesn't think my body will do what it's suppose too, and I'll end up in c-section and he doesn't want to do that. Is there anything I can do to help me get dilated? And what would y'all do? Be induced or wait to see if she comes and have another doctor deliver the baby, or go pass the due date a few days so he can deliver the baby when he gets back?