It's too awkward to just say: Hey, let's have sex!
Obviously, Harry also cares about our FL and he doesn't wanna taint her. You can see it by how he won't even talk about sex as another way.
The other choice is to disrespect someone's boundaries and autonomy, or suffer in silence. He's lived for over 2 thousand years should know how to ask.
Also. She asked what else besides killing would satisfy him, and he gave an evasive answer. He should have told her the truth. He wouldn't even have to mention wanting her specifically at that point. But at least the ice would have been broken.
Maybe he should stop playing around and tell her what he needs???
Like dude if you wanna fuck you're gonna have to ask. How old are you again?