That's fair. As a socially anxious guy, I probably would go for the "If you want" and/or "If you can't/don't want to that's ok" route.
I wouldn't necessarily say that the person on the left in the picture is aware the advance is unwanted, though. Of course, it's an AI picture, that guy does not exist, but speaking of a hypothetical person with even worse social anxiety than even myself, I could see one like that using "Sorry". Not because he knows that the advance is unwanted (though it could be that he knows, it just depends by case), but because he assumes any advances from him will be unwanted. Getting rejected every single time would make it hard to assume "Ok but surely next time will be ok", and so you would operate, from the start, under the assumption that the other person doesn't want to talk to you.
I don't know if my point is coming across too well, but basically what I'm trying to say is this: Once you get to the point where you think every single interaction coming from you is unwanted (which is probably false. Even if most are, it's highly unlikely all are), then you kinda stop differentiating between when someone actually doesn't want to talk to you, and when you're overthinking but you're actually incorrect. So if the guy would stop trying to interact with people he thinks don't want to talk to him, he'd essentially stop trying to interact period.
I wasn't necessarily disagreeing with you. My comment was to show a different perspective, not to dismiss or argue against yours. Or rather, not all of it. Cause I do agree on the "Sorry" VS "opt-out" part.
Here I would add something, though. If this person doesn't see a path to success with any woman, I don't think he should necessarily give up, because at least some of the "There's no way it'd work" would be false. Some will be correct, but because of the constant rejection the guy faced, he will be assuming all are under the "There's no way it'd work"-umbrella. So if he stops pursuing a relationship in general in order to avoid women who will reject him (which, in his mind, would be everyone), it'd become a self-fullfilling prophecy: He thinks no girl would be in a relationship with him, therefore he stops trying, therefore no girl would be in a relationship with him.
To be clear though, I'm not advocating for asking out someone who is actively avoiding you, or someone who already made it clear in some way that she's not romantically interested. Like if you confess and she says no, he should give up, yes. But not before it's confirmed that his suspicion is correct. I've been rejected many times, all times so far, in fact. I have always stopped the romantic approach towards that person once I knew they didn't like me romantically. A couple I'm still friends with to this day. Others that I wasn't particularly as close with before, no, especially once the thing keeping us together ended (as an example, a high school crush after high school was over).