If your pottery all have exactly the same size and shaped bottoms, you could make a shield out of cardboard or acrylic with an opening in the center which exactly matches that bottom. You could then add more cardboard or acrylic on the bottom side of that shield to build up a downward pointing ridge that fits the first quarter inch of the sides of each pot. This shield could then be quickly placed on top of each pot and held in place with one hand while the other hand applies the brush to the exposed bottom. The shield would hopefully catch any excess wax, keeping it from rolling down the sides to interfere with the glazing.
As the wax may gather on the shield after each use, you may need wipe it off after every few pots. Creating a second tool in the form of a towel covered cone which matches the shield's opening and sides, could give you a place to perform that cleaning.
One final improvement to the shield would involve finding a wide brush which can apply wax to an entire pot bottom in one stroke. Once you have such a brush, you can add raised sides to the top of the shield to form a trough to guide that extremely efficient brush stroke.