We can't forget that Sanji was the one who took it upon himself to save Kinemon, and what was the decisive factor for that decision
The determination of a man literally into pieces to find his son.
Now we know that Momonosuke is not Kinemon's actual son, but he took it upon himself to protect him. And we know that for Sanji when it comes to fatherhood blood ties matter less than actions, and through his actions Kinemon was valuing Momonosuke as he would have his own son.
Knowing how much Momonosuke means to Kinemon, he's very likely to want to make the choice Kinemon would have made.