This isn't a vote, necessarily, but I'll try to make a potential argument for Minato.
The AP gap isn't really big here, and from what I understand it's in Minato's favor, especially in Sage Mode. I think he'll be able to tank a couple of hits, and once he figures out that he's up against an invisible opponent, he might try to mark him with a FTG seal. At which point, the fight will become a lot harder for Sanji because Minato can instantly teleport to his location whenever he chooses, which limits his evasive options immensely, and with an AP advantage favoring Minato it becomes even worse. This type of strategy is completely in character for Minato as well, so I really do see him attempting it.