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Bringing back something I wrote seven years ago back on Reddit:
I have an appreciation for Jon's ability to manipulate and scheme. From his first scene in AGOT he showed a gift at manoeuvring a situation into his favor, but the baby switch cements this ability the best I think.
First, its important to note that Jon doesn't rush into his lie and swap out of nowhere, he lays the groundwork and plans meticulously.
“Sire, some claim that you mean to grant lands and castles to Rattleshirt and the Magnar of Thenn.”
“Who told you that?”
*The talk was all over Castle Black*. “If you must know, I had the tale from Gilly.” - Jon I ADWD
He says something of which he'd heard rumors of, but he assigns the blame to Gilly so as to alienate Stannis further from her. By doing this, he deliberately leads Stannis into the conversation where he can mention sending Gilly off without drawing any attention or reprimand from the king who practically controls Wildling lives on the Wall.
“The wet nurse,” said Lady Melisandre. “Your Grace gave her freedom of the castle.”
“Not for running tales. She’s wanted for her teats, not for her tongue. I’ll have more milk from her, and fewer messages.”
“Castle Black needs no useless mouths,” Jon agreed. “I am sending Gilly south on the next ship out of Eastwatch.”
Jon is very good at reading people, and he uses that to his advantage by associating Gilly more and more with the things he knows Stannis dislikes and he does it covertly.
The king was confused. “I thought the wet nurse was this man Craster’s daughter?”
“Wife and daughter both, Your Grace. Craster married all his daughters. Gilly’s boy was the fruit of their union.”
“Her own father got this child on her?” Stannis sounded shocked. “We are well rid of her, then. I will not suffer such abominations here. This is not King’s Landing.”
He plays on Stannis' prejudice to achieve his goal.
Finally-
Melisandre : “Gilly is giving suck to Dalla’s son as well as her own. It seems cruel of you to part our little prince from his milk brother, my lord.”
Careful now, careful. “Mother’s milk is all they share. Gilly’s son is larger and more robust. He kicks the prince and pinches him, and shoves him from the breast. Craster was his father, a cruel man and greedy, and blood tells.” - Jon I ADWD
The above is what he says but in the next chapter this is what he thinks:
Gilly’s boy was older, Dalla’s more robust, but they were close enough in age and size so that no one who did not know them well would be able to easily tell one from the other. - JON II ADWD
He will die at sea, he thought, despairing. He is too old to survive such a voyage. Gilly's little son may die as well, he's not as large and strong as Dalla's boy. Does Jon mean to kill us all? - SAM I AFFC
Jon even swaps the physiques of the babies when describing them to Stannis in order to confuse him further and eliminate a chance of them being identified correctly. He further uses that incorrect physique to push the rhetoric of Gilly's babe being an "abomination" covertly to Stannis. Jon hammers out the details of the lie meticulously, not leaving any scope for failure by being vague. He goes all the way.
I think its an aspect of Jon's character people don't notice or credit much because it isn't at the forefront the way it is for Tyrion, but he too is capable of playing the game. I don't understand when people dismiss Jon's abilities in manipulation or write him off. He's often navigated such situations masterfully and shows himself great at reading people and what moves them from the very first book.