Yojimbo's chances of using Zanmato depend on how much you upkeep him. Using him every second battle and paying him a minimum of 1000 gil everytime was my strategy. Did that for about 15 mins before I fought every Dark Aeon. After a while, Yojimbo would upgrade himself from Kozuka to Wakizashi. When he starts using Zanmato of his own accord, that is, without paying him first, you know you've got a friendly Yojimbo.

You have to maintain the relationship, it diminishes if you don't use him enough. Moreso if you pay him little to nothing. If he Daigoro's, don't expect much else from him but that and Kozuka until you start paying him some hard cash.

Note that it is also random to a certain extent. So don't complain if he still uses Daigoro and random Kozukas when you don't expect him to. It's usually a one off though.