So close. SO CLOSE.
I'm asexual, but not aromantic, and I have a long-distance relationship going on (with a man, if that's important. I'm a woman). Relationships are about more than sex, and if both you and your partner are willing to go without, more power to you and to them. As my boyfriend is heterosexual, and as this relationship is long-distance, I wouldn't be angry if he fulfilled his sexual needs in other ways. Hell, I wouldn't be angry if the relationship was face-to-face.
However, you don't choose whom you love, and there is no "wrong type" of love. If, hypothetically, two heterosexual men were to get married and never had sex with each other, would that be wrong to you?