I was filling out a ship chart and in doing so I've realized how different Hanako and Kou would be in a relationship with each other instead of their more canon companions. I know this sounds very obvious like yeah ofc all relationships are different but like...the biggest distinction to me is how much they would fight for each other. Canonically Hanako is very possessive of Nene and Kou is the same with Mitsuba. Neither of them want someone else to save the one they love because they both want to be recognized for their efforts in some sense. Hanako is selfish in a very straightforward way: he makes big decisions on others' behalf without their consent in order to "do what's best for them" even at the expense of others. We see this in how Hanako tries to extend Nene's lifespan multiple times over the course of TBHK. To him, helping Nene's wish come true by any means possible is his final act of love and "redemption" of sorts. As for Kou, he's more selfish in an underhanded way. While he's known for his altruism, his eagerness to help others is born out of a need for validation. We see this in how Kou refuses to exorcise Mitsuba despite his dangerous appetite. He won't let him go because he likes having someone depend on him. In essence, Hanako and Kou both fight tooth and nail to keep their respective partners alive because their partners' existence fulfill something they lack.
Now if Hanako and Kou were dating each other... this possessiveness and grit nearly dissipates. In my mind both of them go into it knowing that Kou will be the one to exorcise Hanako and that is final. Maybe dating Hanako would make Kou waiver a little like he did in the young exorcist arc but ultimately he knows where he stands with Hanako as a whole: he isn't the totally evil apparition his family told him he'd be but he's not a good apparition either; he's done unforgivable things and continues to do so through his own free will (ex. Sacrificing Aoi). Circling back to canon, Mitsuba is ultimately someone Kou can side with despite the danger he poses because so much of his own self worth relies on the Mitsuba's existence. Hanako, however, is hyper independent and has shaky morals that are harder to justify keeping around. Kou can't fall back on how he feels personally about Hanako to say "I'm not going to exorcise you" because Hanako doesn't need him in the way Mitsuba does. If it comes down to it, I believe that Kou would be much more willing to exorcise Hanako than he ever would be with Mitsuba even if he was dating the former. The example below shows exactly how Kou views Hanako: it's very matter of fact and blunt.
As for Hanako's side of things... there's no chance that Hanako is as nearly of possessive of Kou as he is with Nene. Kou isn't the one with a shortened lifespan nor is he totally helpless in supernatural circumstances. Sure, he's weak in comparison to his brother and reckless in matters of self preservation but Hanako knows Kou has enough will power to tough it out. It's one of the things he likes most about him after all. In my mind Hanako knew from the start he would have to be exorcised someday but he never had a preference for how he went out. That is, until Kou entered the picture and Hanako entertained the idea of his death being at the hands of a brash hero-wannabe. He saw the potential in Kou and that's what mattered most. Only when they began dating did Hanako's indifference towards his dying method shift to insistence that it has to be Kou. As long as he's fulfilled his duties, Hanako won't fight Kou when it comes down to it because he's already accepted this a long time ago. I struggle to say definitively whether or not Hanako would be willing to sacrifice himself for Kou as it stands regardless of their relationship status because unlike how he views Nene, Hanako has enough faith in Kou to let him figure out his own fate. The example below is much less serious than the grim reaper arc but it's one of the earliest cases of Hanako letting Kou handle himself instead of helping him because he believes Kou can do it ("you're doing great!").
Essentially what I'm saying is that I don't think either sides of Hanakou would be willing to go the lengths they do for their more canon companions to keep each other alive. Hanako is too independent for Kou to justify keeping him around and Kou has too much agency for Hanako to try saving.