You’re in a very very difficult situation here. What is your partners reasoning for contact? Does he not believe his father is a sex offender? Or does he think he is, but because of his loyalty still wants to keep some form of contact?
If he doesn’t believe it then you’re in an even worse position, if he does believe he’s a sex offender you can at least attempt to reason with him for no contact.
The problem with any form of contact is it’s a slippery slope, if it’s okay for your father in law to have contact because according to the whole family and your partner he’s innocent and poses no danger, then it will be okay for cuddles, then it will be okay if your partner just nips out to the kitchen or toilet leaving FIL alone with your child. Are you willing to speak up and refuse grandad cuddles with your child in front of the whole family (and your child) who think there’s no reason why he shouldn’t and explain why? Do you think your partner is going to follow your agreed rule that your child can’t be alone with grandad even for a few minutes when he goes to the toilet or kitchen? That your partner ever can’t take your child to see grandad without you? That Nan and grandad can’t babysit your child for a few hours alone?
Remember that you will not just be going against your partner here, you will be battling against a whole family who will be pushing for this and will be highly offended by your very reasonable explanation that you don’t trust your FIL because he’s a paedophile.
It’s an emotive subject and you’re dealing with a whole family of deniers and enablers, supervised contact for the next 18+ years meaning he is never ever alone with your child and never has any physical contact with them is going to be impossible if your partner has a relationship with them and sees them regularly. Kids are innocent and won’t understand that they can’t go up to grandad and have a cuddle.
The only realistic option here to guarantee your child’s safety is no contact. I would advise you to try to get your partner on board with this as there is a big risk with expecting the court or SS to protect your child as your FIL has no convictions. Leaving your partner off the birth certificate only buys you time, if he is determined enough he can prove paternity with a DNA test and gain access. I would try to get your partner on board and speak to social services about your concerns. Going along with this supervised contact plan is not realistic and puts your child at great danger.