I am pretty much the same here. I do not have genital dyphoria, but it's doesn't mean I like it. It just, genital doesn't matter. And I like man and never use my genital for having sex (it doesn't work anyway from long time anti-androgen). And my daily life is totally a woman, so for me getting sex-change will only slightly make the different and that different is only me who know. I also more concern about general appearances.
The only moment that I wish I have done sex change is when I have to wear bikini, but it's not a big deal, I didn't wear it everyday and tucking is not that bad.
I use to want to have srs, but after sometime living as a woman, I decide to stay this way, where I am happy now. Even though all my trans friend getting srs. And I took care all of then when they get it. So you are not alone there

and there are more openly non-op trans like Buck Angel, he also come out as non-op too.