There are few events where Wanda brought up the full moon's connection to the minks. She hinted at the full moon having some form of dangerous effect. Since the moon's relevance was never explained on Zou, I still believe we will get more info on it. It could have to do with Zunisha itself, but then I saw this, Inuarashi stated recently that the Minks have somewhat of a trump card that they didn't use against Jack for some reason. Since they fought for multiple days, why wouldn't they have used this secret ability?
But if we can connect what Wanda said about the full moon to the Minks, it's possible that their powers are conditional, and they only work when the full moon is out. Zunisha always covered up with fog, and this was the reason the full moon was covered up the second time when Wanda spoke of it. But the Minks are now leaving Zou, meaning the full moon can now affect them easily if there's no clouds to cover it up. And even with the obvious hint at the full moon being relevant, how could it actually affect the Minks? Each race in OP seems to have some special power. For example, the Fishmen are able to control liquid. And they can control the energy related to races' theme, water. We know the Minks have a special power, electro, which is one of their races' specific abilities. But we don't really understand it. Just like the full moon, it's possible that the sun can affect their bodies as well. Making their body somewhat of a solar panel and can transfer the solar energy to generate electricity.
So while the Fishmen can control the energy of the sea, the Minks may control the energy of the sun and the moon. An example of how someone was affected before by lunar energy in OP, it has also been shown that it can affect Kuro, who was stated to have gained bloodlust from the cresent moon. So while the Minks may normally use electro, potentially fuelled by solar energy, which is at its peak during the full moon. But as Wanda hinted previously, there could be some form of danger to this ability. Since Minks are half animal, their inner animal instincts may be controlled by this dark power. And we've actually seen examples of this.
The first example of this is when we saw Carrot attacked Luffy over a carrot, her eyes turned white. While this can be argued to be comical, it gets even more mysterious. The other Minks hinted at Pekoms needing to be "controlled", implying he may have some dangerous power that he cannot control.
These two specific examples may be hinting at some form of "weremink" rage, where they become more animal-like and lose control of their human traits. And even moreso, Ceasar, when arriving on Zou, even said that the Minks ere described as dangerous barbarians to him. It may have been a case of the WG exaggerating it. But maybe there was a point where the Minks were actually much more barbaric due to this power consuming them. What makes this even more convincing is that Nekomamushi explained that he was a monstrous human-eater. But then later on showed to be a very kind-hearted person which may be hinting that they have some form of split personality that even they are aware of.
And then there's the mysterious split between the dukes. When they went to the outside world, their lack of self-control may have led them to become much more hateful and bitter. Since cats and dogs are natural enemies, their animal-sides may have clashed over time. Pekoms, one of the few Minks that we've actually seen go to the outside world is described as "uncontrollable" and needs to be supervised. How come all the Minks that have gone outside of Zou become much more barbaric over time, it could be because Zou was created as a safe spot for them to control their "animal" side which was seen as barbaric by the WG. Zou has that fog around it which conceals the moon and the dukes also have the day and night cycle which was maybe intended to keep this under control.
So for these reasons, I expect the minks to reveal this "trump card" which may be an advanced version of electro and can tie into the full moon effect that Wanda brought up.
http://www.mangareader.net/one-piece/805/13 Wanda's conversation in 2nd panel
http://www.mangareader.net/one-piece/811/5 Ceaser's conversation in 2nd panel
http://www.mangareader.net/one-piece/811/18 It's full moon
http://www.mangareader.net/one-piece/819/8 Trump card 5th panel
http://www.mangareader.net/one-piece/28/6 Cresent moon
http://www.mangareader.net/one-piece/819/17 5th and 6th panel Pedro talks about Neko's and Inu's journey
http://www.mangareader.net/one-piece/822/12 three last panel KEEP HIM IN LINE
http://www.mangareader.net/one-piece/823/16 and 17 Carrot attacking Luffy