You are (both, but you more than him realistically) facing into a long period (measured in years, and varying depending on how many DCs you go on to have) where you will have to miss opportunities because if responsibilities at home.
You need to weigh the importance of the opportunity, both professionally and personally for him, against the chance that him being away at 37 weeks will present a problem. And when you do, bear in mind that life is about to get a lot more complicated. It won't necessarily be easier for him to take up a chance like this once the baby is here, even if it does come up again.
Also, if he's like my DH, he won't be seeing the risks you are seeing, because the whole thing is an abstract concept rather than a daily biological reality :)
If you really, really need him with you, then don't be afraid to ask for that. If he's a good guy he'll put his pregnant wife's feelings in late pregnancy first, even if he doesn't understand them.
Don't feel sad that he doesn't feel the same way as you do. How could he, really?
I guess what you really want is for this never to have come up as a possibility, so there would be no decision :)
It is stressful trying to make plans when you are facing into the completely unknown.