It seems like you're in your head about a lot of things.
I can relate here because when I first started daygame, oh, man, I was so fucking
terrified of accidentally hitting on a minor—I'm old enough to be their dad!—that I had trouble getting myself to approach anything under 30. This was
especially hard for me because I love black women and black girls get booty
fast—I knew a tall 14 year old black girl that
easily passed for adult (until she opened her mouth).
You have to realize that there's nothing abnormal about being attracted to a female that has gone through puberty, it's just nature! Go to the Wikipedia article for Puberty, there's a set of nudes of the typical girl from childhood to the end of puberty. The last pic is of age 16.0, and is straight up an adult body. Even the 15.0 is so close as to be well within the variability of adult females (not hard to find 30 year olds that have the same physique).
Obviously don't go approaching minors on purpose, but my policy is that if I like the girl but I'm not sure she's of age, just approach her and find out by talking to her!
Initially it's really scary, you think like an underage girl is going to scream at the top of her lungs and spray Mace at you until the cops come and put you away (even though you didn't do anything illegal). Now I've done it enough times, I can assure you that won't happen. Usually, if anything, they are flattered and happy to chat.
Only thing you really have to worry about is that she might lie about her age because she wants you to fuck her. Which is why I don't even ask directly. I ask other questions that she's not going to have good answers for on the spot. After talking to her a couple minutes you should be able to tell if it's a high school chick vs. uni chick or whatever.
I mostly game in stores in large malls. Nobody is checking ID at the door, so yeah, if I approach 10 girls, typically 1 or 2 of them end up being high school chicks and I just move on, it
really is no big deal, trust me—and I am older than you.
Fuck, a few times I've hit on what turned out to be a high school girl
with her mom right there! Fuck me, hahaha. (
Obviously I didn't
know the girl was underage or I wouldn't have wasted my time approaching.) So far in these situations, mom didn't say or do shit. In one case (African) the mom just smiled and wandered off.

At least once I would've been of half a mind to hit on the mom once I found out the daughter was too young, but I haven't quite done that yet.
(Whether to count these as approaches, I never even thought about it before... I do count them, simply because I still had to pick up my balls and go talk to the chick. Obviously seducing her is off limits, but that's just built into the ratio, which will never be 100% anyway.)
I'm glad I don't let it bother me, because the first chick I laid from day game, actually she was a college girl (100% sure, I helped her with her homework afterwards), and with a fairly nice body, but I had been scared she may have been a high school girl but I approached anyway.
If you're not attracted to the girl, obviously don't bother approaching. Sure, I pass up adults who have no booty or are really short, just because I don't find them sexy enough.
But if you
are attracted but somehow it's still "off putting which leads to an awkward approach", this is
totally in your head. I've (accidentally) approached an attractive high school chick quite a few times without any awkwardness, save for the disappointment that she's too young. Just, "well, it was nice meeting you, Keisha," and I'm off. You
make it awkward by thinking about how terrible it is.
This is an assumption that does not help you.