From memory, they are mini pots...quite a lot smaller than standard. I've put EMG's in a few Brandoni/Japanese bodies and although a bit tight, its always worked fine. Worst case is getting the cavity deepened a mm or two, which wouldn't cost much to have done. You may also find that if you ask a luthier to supply and fit, he doesn't really charge for the fitting.
There are also some very good passive humbucker versions around..Aguilar, Nordstrand etc which don't need a battery and would be pretty quiet in use.