For me, this is a very confusing statement, if it is not an ultimatum.
I informed WH that I would not stand in the way of him having a relationship with OC if that is what he wanted, but it could not be with me by his side.
I could interpret this two ways.
The first way I could interpret it is to hear you say, "It doesn't matter if you have a relationship with the child or not, I won't be here either way, the marriage is over."
The other way I could interpret it is, "I'm not staying with you if that child is going to be part of your life. If you want me to even consider staying, then a relationship with the OC is out of the question."
If what you meant was first interpretation, then I find it confusing because I'm not sure what his relationship with the child has to do with anything if that's the case. If you are leaving him no matter what, then his relationship (or lack thereof) with the OC is not pertinent nor germaine to the fact that you are leaving. You are leaving because he cheated, not because he may or may not have a relationship with the OC. Do you see what I mean? Why even mention it in the same sentence if it's not a precondition of some kind?
Imagine if your boss said to you, "Well, you can take a long lunch break if you like, but don't expect your job to be here when you get back". Does that mean you're fired? Or does it mean you're fired if you take a long lunch break? If he was just firing you, then why say something such as "Do what you want, but..."? He would just say, "You take too many long lunch breaks, you're fired".
If it's the second interpretation, then I don't see how it is anything but an ultimatum. If you are willing to stay if he doesn't have a relationship with the OC, and not willing to stay if he does, then that's pretty much the dictionary definition of an ultimatum.
Just to be clear, I'm not trying to put any kind of judgment on your decision. You have every right to stay or not stay with him for whatever reasons you like. He could have avoided all of this by not having an affair. And even if it is an ultimatum, that's your right as well. He offered you an ultimatum by having an affair in the first place.
For your own peace of mind, I would suggest taking a closer look at what it is you really want, and what it is you are trying to say. To me, it sounds as if you are struggling with a profound amount of second-hand guilt over this child. On one hand, you know it is simply untenable to be in a relationship where you are forced to interact with a child because of your spouse's infidelity. That's unfair to you, and any other family members. At the same time, you also realize that, like it or not, this child is still a child and deserves the presence of their father in their life. There is no "right answer" here because someone gets hurt no matter what, hence the feelings of conflict or guilt.
I dunno. It does sound like an ultimatum to me. Sorry. I know that's not the most popular answer here. I don't think it needs to be an ultimatum however, I just think you need to decide whether to stay or not and not tie it, in any way, to his relationship with the child.
Last thing, in my mind:
A boundary does not have conditions. An ultimatum does.
Boundary: "I won't work at a job where I am demeaned".
Ultimatum: "I won't work at a job where I am demeaned unless I make at least a million dollars".