Check out Kenny the Pirates website. I'm not sure when and how often they come out anymore. About 10 years ago or so they were regularly by the Teacups, but that website lists the characters and their normal schedules.
We came across them at the end of January!!! They were hilarious and a great interaction outside the teacups with Alice and the white rabbit, but meeting separately
I saw them twice on my trip last week, once in the morning by Tea Cups, don't remember the exact time but it was before 11 I think, and once during the half marathon (so that doesn't really help you). But it sounds like your chances are pretty good!