This website gives you the probability of your child being born on any given day. It has great breakdown of the probabilities over time, and takes into account whether he’s been born yet (i.e. the chance he’ll be born on a particular day rises as you approach that day, and he hasn’t yet been born)
So, given Oscar hasn’t been born yet and is due on Jan 29, there’s a 2% chance he’ll be born before Saturday: the day of his baby shower.
Confusingly, that probability will decrease tomorrow. Tomorrow, he’ll be more likely to be born on Friday (since he hasn’t been born today) but there’ll be less time between now and the baby shower, so less chance he’ll be born before the baby shower.
