Oh the cories won't bother them! I put newborn guppy fry in the same tank as my cories 'cos cories are such sweeties, they're not out trying to eat fry
They might accidentally eat their own eggs and fry, but that's derpy rather than predatory, and guppy fry are more than capable of avoiding even when newborn. They'll be fine, let 'em out! You should get someone to film you releasing them from the box into the tank, it'll be cute! Then upload it to youtube and share the link here
Before releasing them, feed the adults, and give them time to settle again, so they're full, but not still actively hunting for food. Not because they'd eat the fry since those are large enough, but just because if they're hungry it's natural for them to chase, and you'd probably panic
If they're full and not in feeding frenzy mode anymore, it should hopefully go more smoothly