In my experience, most CofE churches will expect you (both parents) to come along to one or more meetings before the planned baptism to talk about what it means, why you want to do it, why the church thinks it is important etc. It's not something that you just book, turn up on the day, and then forget about. Or at least churches don't want it to be that.
You are agreeing to raise your child in the Christian faith, with an aim of getting him/her to decide to be confirmed when old enough. You have to stand up in front of the vicar, the godparents, and usually the whole congergation and say things about believing in God, Father, Son and Holy Spirit and raising your child to do the same.
Your FIL is being unreasonable in asking you to stand and lie in front of everyone, when you have no intention of raising the child as a believer. If he genuinely plans to do that, and you're ok with it, then he could stand there and say those things and you just stand there being silently supportive of his intentions.
Otherwise I would definitely say go for a blessing/thanksgiving service instead that way the vicar will just say things about how great the birth of a baby is, and say prayers for you and baby, without you having to lie about what you are doing.