Though I guess it depends on who ever is following and how open to such ideas they might be...
Well things to ponder I guess...
We basically got that answer from the QM's comments on what would happen with the current vote - the person following is "Kana", which is why asking who the pursuer is, is going to result in her spilling Kana's inner weaknesses.
Though if take what the Shadow said at face value, the Kana that is about to come after them is going to be angry immediately anyway, regardless of any secret-spilling.
Why exactly she would be angry without prompting is a good question. The reason I thought "normal Kana" was unlikely to be the pursuer was because "normal Kana" is generally pretty friendly and reasonable- and then the QM gave this cagey response about Kana's normal persona, in regards to it:
Not a direct reply:
A Shadow represents the parts of yourself that you reject, but they still exist. Fully rejecting it, and making that stick, would turn you into a caricature of yourself.
This could also be compared to the effect of boosting a virtue up to five dots, then hitting limit break. Inverted, in a way, but it's the same concept—take just one side of yourself, present it in its "perfect" form and ignore all else.
Amu likes the confident, outgoing side of Kana that wasn't broken down by reality… but she likes it because of what's inside, not despite.
I don't know exactly what to make of that, but it was one of the meta things (the idea that Kana has rejected a certain part of herself to an extreme extent) that made me elevate the Yui-is-Kana's-Split-Personality theory a little bit. Along with the QM previously also giving a suspicious "no comment" during last vote when I concluded the stunt wouldn't result in a room with Yui in it.
But that theory aside, my best guess as to why "normal Kana" would immediately be mad is because this cognitive-space intrusion might be reminiscent of her experiences at Manticore, causing her to elicit the same kind of extreme temper response she had for the man whose mind she crushed on a whim. Or even worse, betrayal at the thought of someone she trusted digging around in her cognitive space (the person this time being Amu, it might have been her trusted doctor before).
We might be able to defuse it if Amu can use her Empathy to broadcast the exact reason why she came in (worry at her not responding to calls).
But that's only if that guess is right. Conditioned/brainwashed by Manticore or driven insane by the fog are still on the table, in which case she might be too unreasonable and unreceptive for it to work without first exhausting her, like one would normally do to a bulked-up Shadow in Persona 4.
I don't have enough nope for this, so (hopefully Pistachio is available soon so we can hash out something else together):
I would suggest having Amu telepathically share the information with Utau and then just having Utau do the projection, if you want her to be a "filter" for things conveyed to Naoto.
Though given Utau's reactions to her Ragged Crossroads visions, I do wonder if Utau would have the stomach for that task and/or whether she might end up redacting 90%+ of the whole thing.
(Also, Amu apparently wants to look cool and delegating the task to Utau makes her look less cool.)