Really, if it had happened to someone you would know at least one grandma who was still pregnant. C-sections only became safe enough to be a viable option over labour in about the 1950's. Before then it was much more life-and-death.
Bear in mind that for me i WAS dilating and i still went 11 days over. I have a friend who just had #3, she was dilated to 4 at 36 weeks and just had her baby at 42+4! Your Ob is LOOKING for problems, because it's his job to solve them if they occur. This isn't a problem. If you'd been posting this after 36 hours of relentless, painful, strong contractions i would wonder if there was something going on (even then, most likely is fear, which inhibits the dilation of all sphincters, or an induction done before your body was ready to deliver). But now? No, your cervix sounds completely normal. As for him saying it like you SHOULD be doing it now, well it's possible he never meant you to think that at all, and it's possible he DID mean you to think that (though probably not very consciously) purely because he knows a drug he can use to make you dilate. It's a bit like a beauty cream ad drawing attention to wrinkles - normal, everyone has them, suddenly presented as a problem so you'll buy into the "solution", the wrinkle cream. He has a solution to non-dilation, even if non-dilation in your case isn't a sign of a problem.
It is really super common to have these thoughts at the end of pregnancy - i know i did! By 41 weeks i had decided i was NEVER going to give birth at all. And she eventually did come out
In retrospect i think my kind of irrational anxieties about that were the beginning of the emotional changes which heralded labour. So hang in there!
In terms of exercise at your stage i would be walking because the motion of it bounces the baby up and down on the cervix, which WHEN it is ready to begin to soften, will help it to do so. Also because walking involves getting out and about which i think is better for mind and soul than stationary exercise - my preference only!