I'm not trying to be negative but i don't think you will be physically ready to take those classes.
Congrats on both your big events! There is a huge difference in health outcomes between 37 weeks and 39 weeks. Plus induced labors can be longer and more painful and more likely to end in c-section. I would first try to adjust your school schedule rather than the baby's schedule.
Can you ask your school if you can get materials in advance so you can be ready to miss a few classes? What about deferring your admission to a later start date? I am sure you are not the first new mom to be in this position and can find someone sympathetic in the admissions office...good luck!
babies come when they want:( but there is couple ways that they can help get them out faster . my midwife will stripe my membranes at my next appointment 39w3d, my frien dr did it at her 38 weeks appointment. you have to talk to your dr or midwife about it