I've thought about this more and I agree with you that I will be fine this summer, assuming no complications. I have decided not to talk to my supervisor for a while. I will be able to work without asking for any modifications. And I just found out that I have a coworker who is due only 4 days before me! She is on her second pregnancy and does not seem worried about working this summer, so that reassured me as well.
But I did cave and tell my friends