Well if Crocodile can touch him he can just drain him of moisture, but somehow I doubt that he could do that through the Raiton shroud. A sand storm might do something, but he'd have to get his hands on some sand seeing as he can't transform, so yeah, I don't think theres anyway for Croc to win without intangability.
One way would be to create a sinkhole, but he just won't have enough time.
I cannot recall the technique, but I will take your word for it.
Regardless, Crocodile was able to physically combat Luffy, who is stronger than Raikage physically and at least as fast at base (Which is giving Raikage the benefit of the doubt), coupled with his sand powers he should win IMO.
Raikage has enhanced speed with his aura -Sasuke's chumps couldn't keep up with him?- but unless he knows about Crocodile's weakness to blood/water, he won't put him down before Croc does something nasty.
Edit: If I'm correct Haku can hurt logia users as if they didn't have elemental abilities -hit Smoker and an admiral, hurted Luffy as if he wasn't made of rubber-, so maybe chakra works the same way too?