Sanji ain't beating Kuzan solo, unless RS come back AND it's a multiplier type tool.
So realistically, if SH vs BB ever to happen, Sanji & Yamato vs Kuzan.
Why?
1. All Sanji fights have theme
One of them is opponent having the same or opposite trait as him (eg Mr 2 as martial artist, Wanze as cook). Kuzan Ice, Sanji fire.
2. Sanji's post TS fight is a mirror or happened in preTS
- teamed up against a giant : Oars-Wadatsumi
- oppose a Warlord : Crocodile (via brain) & Doffy (via strength)
- fought against a (leg based) martial artist : Mr 2-Vergo
- fought a gang leader : Duval-Bege
- fought a woman : Kalifa-Black Maria
- fought a zoan : Jyabura-Page One
- fought an invisible pervert : Absalom-Queen
- fought a food themed chara : Oven-Wanze
Kuzan kidnapped Pudding, like Absalom kidnapped Nami.
My agenda : SaPu shipper here, I want rescue story arc, where Sanji burst into (all) blue flames.
Why Yamato : Sanji can't solo Kuzan. Zoro will get solo fight. Jinbe is hard countered. Yamato is both strong enough & resist ice. Fighting side by side with Yamato is like a bonus strength for Sanji, especially if the purpose is to fight Pudding's kidnapper.