What mood and character's perspective & emotion do you want to portray? I see that you only say that you want it to be not exploitative, but what's exploitative in this context? The only thing I can think of is that you don't want to make light of childbirth as well as avoiding giving inaccurate infos about it. So yeah... no joking about getting kicked in the balls is worse than childbirth in the next chapter.
And call me stupid for not understanding you, but I don't see how these options can give you a bonus point to avoid making a exploitative and insensitive scene. Though I'll still give some pieces of my thought. Related to my first question, in this story, how deep do you want go with narrating characters' psyche?
The realistic way may be the best way in general if you do omniscient third person. The event and characters' emotions are laid bare whether happy or complicated. The matter of clinical details is honestly depending on how much explicit do you wish it to go, because to me, just the descriptions of someone hurting in childbirth is already realistic enough. Don't meander, decide on specific emotions and atmosphere, and keep the narration in that condition, otherwise, it'll just cheapen the scene, and it may accidentally come off as insensitive to readers. And I must say, clinical way can also be symbolic if you implement it right. You can narrate the visceral experience of a childbirth in a certain character's perspective and make it implicitly known about that character's emotion about it. Someone watching from the side line, and they can't think about anything but the horror that their other half's currently undergoing... sudden guilt, can't think straight from the blood, not daring to think about the possibility of their partner might die so they put aside their emotions under the clinical descriptions, etc. If it's the narrator who's undergoing the childbirth, the over descriptions may give out their emotion about the whole situation, regret... happiness... losing their sense of humanity... some pain is worth it... and so on.
To me, subtle way is interchangeable with realistic way (although it's fine because there's context, joining realistic and clinical way is still a bit restrictive), because both must follow from how explicit do you wish it to go. Skirting around some details is absolutely fine as long as you don't accidentally imply 'this certain step of childbirth isn't important and doesn't deserve to be talked about'. You can try to see if focusing on before or after the childbirth can work in your story. The panic/expectation that's happening as the character's moved to hospital/place to rest. The gloomy portrayal of the woman's bloodless face, lying, facing the ceiling with empty eyes. The joyful dialogues between the parents picking a name for their newborn baby. These scenarios aren't insensitive in anyway even if you decide to lessen the focus on the childbirth process.
For the symbolic way... well, you guessed it, it depends on your writing style and the perspective! I can't give you scenario examples or what it represent like above here because symbolism and metaphor are much more harder to be railroaded by other people. Between the three options, I like symbolic way the best, but who's to say I would like YOUR symbolism? (this can still happen in other option ofc). So anyway, I'm giving you some recommendations. I like these, and they can also be writing materials if you also like them. Though it isn't about childbirth, 'Hills Like White Elephants' by Ernest Hemingway is full of symbolisms, one of its interpretations is about motherhood and abortion, it's really really a great example on symbolisms. There's also 'Indian Camp' by him, which is about childbirth process in clinical way, another good example. Although this is a poem, 'Metaphors' by Sylvia Path is also a great one (this was the first thing that came to my mind when I opened the thread). Though this one is more from a darker approach of childbirth, so beware.
Decide on what's necessary, and make whatever portrayal you want to make as earnest as possible. Don't pull punches.
Ask yourself, is it conductive to your work? If yes, then all three options work.
