What does Ned do if Jon is born with purple eyes & silver hair, assuming Lyanna's dialogue is no different? Since she apparently died before naming him, it's likely (and understandable) that she wouldn't have the chance to note or think of any issues like that, or consider the scope of what she asked Ned, so I think she'd make the same request even if the baby was clearly a Targaryen.
I tend to think that Jon being born with the classic Targ colouring is the only thing that could convince Ned to raise him away from Winterfell, possibly with Howland Reed. If Jon had just the purple eyes, or just the silver hair, maybe he’d chance it. (Especially since Ned’s rumoured lover had purple eyes herself.) But both?
As we see in the books, Ned prioritises Jon’s safety over both Jon’s emotional wellbeing and Ned’s own, refusing to speak of even the slightest hint of Jon’s parentage out of grief and fear. If Jon looked obviously Targaryen, that’s a risk to Jon’s safety if he’s living at Winterfell, where all sorts of people come through and see him.