Kojiro is mentioned as a dragon slayer having taken down tons of wyverns in the moon goddess event. He was following Martha around because he wanted to face the Tarrasque. Mash calls the group of 3 dragon slayers. So yes it is canon that Kojiro is capable of killing wyverns and wants to fight an actual dragon.People, before the REGENDARY meme gets out of control, keep in mind that drakes are still dragons, albeit juveniles.
Also, very-high ranked Phantasmal Beasts by lore, and Assassin-trumps-Rider is a strictly gameplay-only mechanic.
Sasaki might contribute, but it'd be Mama Artoria and (honorary) Uncle Cu Chulainn who'd be doing most of the work*.
* - Possible Uncle EMIYA too, if he spams the anti-draconic Noble Phantasms; otherwise, he's a distraction at best.
Mama Rin? Also support-only, unless Ishtar has lore bonuses against said creature types.
Roman also believes the swallow he faced must have been a high rank phantasmal beast because Kojiro slaughters a demon easily in his interlude(that had the ability to resurrect itself) and he considered it weaker than the swallow. Kojiro was flat out disappointed when the demon turned out not to be immortal, just that it had a stock of resurrections.