Well, when it came to natures in the original, the nature would reflect which berries the pokemon would eat and how much the contest stat would increase. From what I get in reading the link provided, It seems there are no such thing as "secondary stats". There are types of reactions, and certain moves that you CAN use in other contests that affect the judge's reaction to your used technique in the contest.
In other words, nothing to do with any other stats than the stat of the contest you're participating in.
Sorry if I devalued your input.