Why not?
Or better yet, just leave out the part where the Hokage ordered it. Tell him you volunteered for the mission because you feel the village is more important than any single clan.
Then at least Sasuke MIGHT decide to hate Itachi still, or he might just hate the Uchiha clan, who are dead, so who gives a fuck. And if Sasuke still decides to hunt you down, you let him. You tell him you understand why he's doing it, and you don't hate him for it.
I just assumed he used his phasing power to phase through the flames. Or teleport them away.
Why not?
How is that any more damaging than telling him: 1) Yes, I killed every Uchiha because MUHAHAHAHAHAHAHAAA!
Or better yet, just leave out the part where the Hokage ordered it. Tell him you volunteered for the mission because you feel the village is more important than any single clan. And while you're at it, explain to him why your life experiences and how your friendship with Shisui Uchiha causes you to feel that yet.
Then at least Sasuke MIGHT decide to hate Itachi still, or he might just hate the Uchiha clan, who are dead, so who gives a fuck. And if Sasuke still decides to hunt you down, you let him. You tell him you understand why he's doing it, and you don't hate him for it.
It's called treating him like a person you actually care about, instead of like a puppet, and then being surprised when someone else shoves their hand up his ass.