Gender as only partially related to dysphoria?

Could gender exist as a social construction separate from sex dysphoria? And that perhaps the reason why we don't see it that way is because binary transitioning is often considered the norm, so those who fall outside of that category might be considered non-binary (or one of the many ways of identifying outside of the gender binary) when in all reality the dysphoria may be sex-related, or related to certain secondary or primary sexual characteristics, in a way completely unrelated to your gender?

For example, could you be a cisgender woman with sex dysphoria in regards to your breasts, but still identify as a woman?

Also, we know transgender people without dysphoria exist. But has anyone sat down and considered why?

I'm a huge fan of the body-modification community, and I'm wondering as technology becomes more advanced, if we won't see a gradual separation of the genders and sex and sex dysphoria.

And for that matter, what makes up gender? Transgender people exist without dysphoria. Transgender people with various levels of dysphoria exist. But is gender an inherent part of a person's (spirit, soul, psychological makeup, etc.) or is it related to presentation? Does gender even exist?