In Hanzo's case, it's best to remember that he's most famous for his exploits as a ninja, who were the covert agents of Feudal Japan, whose functions included espionage, sabotage, and assassination. Ninjas are quite known for their stealthy nature in most forms of popular culture, and with Hanzo being arguably the most popular of real life ninjas, that would make Assassin a fitting mold for his class. 

Hanzo's choice of weapons is [i]mostly[/i] negligible, and if you are referring to the Kusarigama, while it does fulfill the "long-ranged weaponry" requirement for Lancers to have, it's still, in essence, an Assassin's weapon. It is a weapon with both quick kills and sabotaging the opponent in mind. One vital part of the weapon is the kama, which was used by ninjas since it was easy to carry around harmlessly, being a farming implement as well as a weapon.

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As far as Bellerophon goes, I'm sure his parameters would be, to an extent, weaker than Medusa's, especially due to the end of his legend where he was thrown off Pegasus for trying to ascend to Mount Olympus. His myth revolves, however, upon using Pegasus to achieve feats of greatness, the greatest of which would be slaying the Chimera. It is actually stated that if he didn't have Pegasus, Bellerophon wouldn't have been able to slay the Chimera in the first place. 

As far as his power would go, he'd have reasonably lower parameters in certain areas, and lower skills as well. He'd also probably only have one or two Noble Phantasms at his disposal, one of which being Bellerophon (the bridle.). I'd expect that he'd have an A++, or even an EX to using it. That way, he'd probably have to rely mostly on the Pegasus when against strong servants.