Burying his head? I should imagine that most people's active choice would be to keep their private business private.
I don't understand WHAT is going to come out later? There will always be new people coming and going in your life who will find out your little bit of gossip (which is all it is, to anyone else).
I think the person whose business it us most is the unborn child. I suspect he'd rather know himself, but not have you shouting it from the rooftops. Plenty of children accept a step parent as their father when the bio father is absent.
I daresay if someone says "is that your dad?" at school pick up, he'll happily say "yeah" and choose not to start telling everyone "well I call him dad but actually my mum had an affair with my oldest brother's dad, who is my real dad, but I've never met him and anyway I feel like my real dad is the dad who raised me". Not because he's ashamed or embarrassed but because it's too complicated and too Not Anyone's Business. So why do you want to tell everyone? (whoever everyone is?)
My friend's a nanny, always got "oh he has your eyes!" type comments when out. She just said "do you think?
"
You don't HAVE to bludgeon people with the truth, to not be living a lie.
In your shoes, I'd be far more concerned that I was staying with a man who didn't bond with any of his kids and who (it sounds like?) has been violent.
You did something pretty shitty to him, but still - most men don't end up with a caution.