Matthew 1:19, Wouldn't divorcing Mary still bring her public disgrace?

"So her husband Joseph, being a righteous man, and not wanting to disgrace her publicly, decided to divorce her secretly" - Matthew 1:19 Wouldn't Mary still go through disgrace by being a mother without a husband? Specially if she is not a widow. If Joseph would have followed his original plan, wouldn't Mary still have to face public scrutiny for seemingly having a child out of wedlock and more importantly without a husband?