Really in need of some advice

So I'm 39w1d and I'm also a FTM. Here's the problem I'm showing NO signs of labor and I'm 0cm dilated. I asked my doctor how long he would let me go passed my due date and he said a week (I'm due June 13th so that would mean June 20th) but I'm really scared if I go that long I won't be able to push him out because he'll be too big. Mind you im having a boy so his shoulders are already going to be big. I really don't wanna have a c-section and they're definitely not breaking my sons collar bone! Does anyone have any advice?! 😖