Like Southern Comfort, I don't know of a Wyeast strain that is specifically for Berliner Wiesse. That said, if you've found a yeast that is designed for Berliner Weisse, it definitely contains SOME kind of souring bugs (lacto, pedio, and/or bret, I would guess.)
There's no reason to worry that the souring bugs will "jump" from one fermenter to the other - any more than yeasts do. But you should replace any plastic components that the bugs touch, or dedicate them exclusively to sour fermentations in the future.