@joannekwan Miguel is such a great example! And I agree, I'm drawn in a lot more by personality than looks, so this is a bit of a hard question.
So I love cute, sensitive boys. But I wouldn't describe my favorites as "delicate," and I can't even think of any characters I'm into like that right off (though I'm sure I have some). Some are more physically delicate, some are not- all have the attributes of arse-kicking cinnamon rolls, so this may be a bit different than what you're even talking about, and it might not be. Take it as you will.
(Kubo, Midoriya, and Miguel are all totally perfect examples of this for me!)
If I'm the one drawing, I like youthful faces, biggish eyes and eyebrows, and usually short hair. I like to keep it kind of basic honestly- it's all about purity of dem soulful eyes for me.

If I'm reading someone else's work, they really can take any form. Biggish eyes and strong expression are good indicators. Dorian from "Hooky" comes to mind because he's a dapper angel child, but could still turn you inside out if he wanted. He's (almost) always very well dressed and very smiley and I love that about him!
Hello big eyes, strong expression. Lucien from "Humor Me" is outrageously adorbs. I suspect that even at four years old he could kill anyone he wanted though, and get away with it too.

Did I mention I love eyebrows on cute boys. EYEBROWS. I never even got into Cardcaptors but his eyebrows.

But sometimes my favorites have no discernable eyebrows, or even eyes:

(So fashionable but could kick your trashionable)
Rotund and non-human boys are also adorbs. Big eyes, sensitive hearts, kick butts, aw yisss

But quintessential "cute boy" to me, both in design and personality, kind of boils down to this for me:

Dapper but functional- smol and strong- big eyes, bigger expressive power-
Pazu wins all.