Taking on the BMP would not save Zeff's life.
Oda clearly built this as a "no way out for Zeff" if Sanji fights back
There's no "risk", it's as good as Sanji killing Zeff with his own hands if he acts against these conditions.
That's what the story tells us, so that's the fact of the matter. The fanfiction people write to find ways around this is not part of the story.
Just like how Zoro had to capitulate because there was no other way to save Luffy's life in TB, so did Sanji because there was no other way to save Zeff's life.