but its not based on haki, cause he doesnt have haki.
swordmanship is still a physical ability , what we are seeing in those slashes that are cutting down mountains are his pure physical strength. saw it again when he pushed zoro back in the clash.
fishman karate works on everyone (logias included)
but I wouldnt say its stronger . I guess you would say it would be stronger for certain opponents
but for most fighters I think dealing with s-hawk just based on what both have shown would be more terrifying.