It will be a really difficult fight but let's detail each strength
Haki mastery :
Katakuri have the edge with future sight, that an hell ace in the sleeve.
In armament, with CoC coating Yamato have the edge.
Yamato may not touch Katakuri, but the last one may not able to do her signicant damage.
Devil Fruit :
I think Katakuri have a full mastery of his DF, but Yamato's one may be more powerfull as a Mythic Zoan.
Yamato can put a shield, spit powerfull ice blast and possibly even more.
I'll give the avantage for Yamato
Combat Skill :
Yamato is capable of keeping up and tie with her dad, a Yonkou and not the weaker... While Katakuri is shitting in his pant when is mother is in her tantrum...
Unlike Marco and Yamato, he don't even think it's in his reach to stall a Yonkou.
Stamina :
As a Zoan, Yamato also have the edge on this side.
As result, Katakuri is a formidable opponent, but all he got it's future sight.
It's a really powerfull weapon, but may not be enough against engame fighters who are faster, near indestructible or possess wide range destruction power.
Until Katakuri master CoC coating or black blade with his spear, the game goes to Yamato.
With those, it would be a more balanced fight, but without it will just run until Katakuri FS deplete his haki, and then Yamato will stomp him.