It won't be just his family potentially being lied to by him... it'll be the new girlfriend, too. If he's anything like my daughter's father, and actually, my daughter's new boyfriend, you'll be "crazy" and/or "mental" and will only have got pregnant "to trap" him and/or "for [his] money". Men like this are all the same, I'm afraid.
My daughter is 23. She hasn't seen her biological father - as far as I know - since she was 3 weeks old. He was abusive, I was using contraception, yet got pregnant anyway. Even though I had left him before I even knew I was pregnant (my parents went against my wishes, and told his parents - we were 19 at the time), he and his family did their utmost to harrass me "into telling the truth" (ie, that my daughter wasn't, isn't, his). Except I was telling the truth. He refused to do a paternity test and I didn't persue maintenance. He's not paid a single penny towards my daughter at all.
You need to be aware of what telling his parents might unleash into your lives, though. My daughter's biological paternal grandparents, saw her every week until she was 7 - and she refused to have contact with them anymore. They then stalked her through senior school and college, getting their friends children or grandchildren to feed them information. My daughter ended up issuing them with a "cease and desist" letter when she was 19. His sister then began to harrass me over social media. There was emotional manipulation, offers of leaving her money in their wills, blah, blah, blah... my daughter still refuses to have contact with them. There is a possibility that she was sexually abused by her biological father's abusive father, and a certainty that they deliberately fed her foods which she is allergic to. They made my pregnancy, my early years as a mother, my daughter's teen years absolutely miserable. Just because I stood my ground and defended my child's right to choose. As a mother, you have to be prepared to have very broad shoulders in situations such as this, I'm afraid, OP.
And now... my daughter's 23. In the last month or so, she's started seeing a bloke whose ex-girlfriend had his baby. And she's "crazy", and "mental", and got pregnant deliberately, apparently, just to trap him and/or take his money...
He refuses to see his 8 month old daughter, because - and I quote my own daughter here - "he didn't want her, so why the fuck should he want to see her?!"
His parents pushed for the paternity test which proved the baby is his... and he fiddles his earnings to pay the least amount of maintenance he can. My daughter freely admits this.
She can't understand why I'm actually angry with her about her perpetuating the same abuse that she suffered, onto an innocent child. She was that baby once upon a not-so-distant time, and I know, from experience, how difficult/lonely/hard it actually is to be in the shoes of her new bloke's ex-girlfriend (they'd been together since school, too - and my daughter knows the ex-girlfriend as they all went to senior school together!). Whilst I do know that the ex-girlfriend and her daughter are undoubtedly better off without my daughter's new bloke in their lives... I'm incredibly worried about him doing the same to my daughter.
I know you can be the best of both worlds (ie, Mum and Dad) to your son, OP... but you need to be aware of the pitfalls. There will be hostilities flying around, rumours circulating about your motives and questioning your promiscuity. Your baby - who yes; is completely innocent in all of this - may also face similar as he grows up. He may not have a biological father in his life. He might, like my daughter, have a stepfather, who essentially becomes a Dad. I hope that he does. And unfortunately, he might grow up to become everything that you're trying to protect him. You do need to be aware of every angle, every possibility, and know that if your ex can cheapen your reputation... he'll undoubtedly do his best to do so. Good luck, OP.
I think you're going to need it.