Basically, they just omit the use of sponges.
However, I have also heard of people rubbing the back of their own lower pants legs before the contest, so that during the contest (when they have their own dog in the corner) they rub their hands on the back of their pants to get the rub on their hands, and then rub their dog in the spots that he's getting bit. Looks like they're just "massaging" the their dog in the corner, but they're really applying the rub at that point.
Jack