In the 5% chance that Sanji does not get CoC, his answer to regeneration will probably be ifrit jambe. He never used it directly on the Gorosei, only Diable Jambe. When they don't regenerate, they will be confused, and he will say the same gag line "my heart/passion burns hotter than anything."
The othe 95% chance is that Sanji sees Zoro damage an immortal with CoC, and then awakens it himself.
An important distinction between Zoro and Sanji is that Zoro has more intrinsic motivation than Sanji. That is why CoC was a more internal struggle for him and why enma was his powerup (to draw it from within).
Sanji is more extrinsically motivated. Usually his blooms are to protect others, and he gets stronger to compete with Zoro. So if Sanji sees Zoro doing something "better" than him, his response will be to try to one up him.
So no, I don't think CoC is the "only route" for the immortals to be damaged. But it is the "common route." Same how ryuo was the main counter to Kaido's scales (at least 11 fighters used it against him), but not the only one (sound waves, gamma knife, crushing).