Anyways, Nekomamushi said Pedro should be the one accompanying the SH because he would be able to keep Pekoms in line… we are still waiting to see why he said that and if it was another hint of the full moon power up it couldn't be just "berserk mode" (how would Pedro keep Pekoms under control if he was berserker as well?).
I'm pretty sure it's just to make sure he doesn't do anything mischievous or w/e that would make things difficult for the Straw Hats. Since ya know, he's still loyal to the enemy, regardless of his gratitude.
And like you said, even if it was something else, it wouldn't make much sense for it to be related to the full moon, since Pedro should be affected too. The simplest answer is often the best one, where this was just Oda's way of further justifying Pedro joining their team. Then he expands on the whole "keep him in line" thing by showing us that Pekoms used to be a part of the crew that Pedro led. As his former leader, yea, it'd make sense that he could keep him in check.
I don't believe there to be anything more to that, regardless of whether or not Pedro is alive. Because if he's alive, why would his priority be Pekoms at this point? Pekoms has been surprisingly sidelined throughout this entire arc, and even now, he's away from all the action that's converging at Cacao Island. And the full moon stuff seems to be implied that it's something that makes Minks lose control, so that casts even further doubt imo.
Even if Pekoms allows himself to be affected by the full moon (He may take precautions, maybe his sunglasses alone are good enough lol), he realistically poses no risk to the Straw Hats and co. at this point in time, unless Brulee manages to transport him there for whatever reason.