I actually did some reading about this recently; my disclaimer is that I'm not intersex, but from what I understand, most intersex people are still assigned a gender at birth based on biological metrics/what they're "likely" to identify as out of bureaucratic necessity (which raises all sorts of problems, but that's for another discussion) and will consequently grow up experiencing the construct of gender from a system-assigned position within it. Like perisex individuals, intersex individuals (statistically-speaking) often grow up comfortable with their assigned gender, but also often (more than with perisex individuals) come to identify as a different gender from the one they were assigned, i.e. trans.
In zeetheus' character's situation, it sounds like he wasn't assigned a gender, and in that case I think what you said yourself about the terms "cis" and "trans" not being easily applicable might ring true. (I have many characters who are comfortably "what is a gender", as I am myself personally, and I think that's ok.) But to be fair, if he grew up in a cisnormative society--familial environment is far from the only social environment where a concept of gender is developed after all--then he will probably still have an understanding of how society conceives of gender, even if he doesn't apply it to himself, and cis/trans terminology will still be useful to him. The main situation where I can see him needing to "choose a label" is if he wanted to interact with other people in LGBTQ+ spaces, assuming he has reason to. If the gender concepts he is familiar with give meaning to the terms, then they are still terms he can use, even if it's just to explain himself to others.
As for knightofpherae's characters...I actually think it's different from the above, and it depends on angels'/demons' cultural concepts of gender, how they relate to their physical sexual characteristics, and how stable of a gender category "nonbinary" is in their society. We have a gender binary because our cultures and institutions tend to sort us into one of two gender categories based on physical sexual characteristics, and "nonbinary", for us, refers to anyone who falls outside said structurally-enforced binary. It isn't a stable category so much as a term that catches those who "fall outside the boxes".
With the angels and demons in your universe, it sounds to me like instead of a gender binary, they may have a gender...ternary, especially since being born without sexual characteristics sounds like it's as common as being born with them. And evidently, angels and demons do have preferences as to their physical sexual characteristics, which I take to mean they do have a concept of gender. If so, then does an individual who's born sexless get assigned nonbinary (or the equivalent), or are they shoved into either male or female? I think that's kind of the key question; if their society's institutions and cultures treat gender as three rigid boxes, and gender identities still exist on a spectrum in spite of this, then concept of being trans is probably still useful, but "nonbinary" may not be, at least not in the same way we use it. (EDIT: or at the very least, the terminology would have to be different to account for the difference in how they experience gender.)
In this case, I would definitely consider the possibility that the way angel/demon societies conceptualise gender is different enough from ours that terms like "trans" and "nonbinary" may not even be applicable to them, as zeetheus said. Even within humanity, there are numerous cultures in which individuals who defy their assigned genders don't refer to themselves as trans or nonbinary, let alone a society of beings are sometimes born without sexual characteristics. "Transgender" and "nonbinary" are not just catch-all terms for all individuals across time and space who don't identify as the gender they were assigned at birth; it refers to a specific experience of gender in our societal context that falls outside biological essentialist systems of categorisation. Because even things like how gender is assigned, how it is performed, and how it is policed, change when we look beyond present-day Western society.