#1, the following link to a fellow who makes (or at least once did) a special zapper designed for pets. It's a collar to be worn around the neck. I personally have not used this product, having opted for #2, but the info from this web site may be of interest to you. PS - his people Zappers are constructed of a size/case similar to the Croft design.
#2, you no doubt are aware that one of the significant hindrances to pet zapping is hair / fur, coupled with the handhold-type contacts with Clark Zappers. I have not yet tried the Clark Zapper, instead using a Croft model. If you are not familiar, the contacts (two pennies) are fixed to the Zapper itself, which is a small box - a plastic case, a bit smaller than a pack of cigarettes. This design allows the Zapper to be placed on many areas of the body. On my dog, I've found the least hairy spot is on the underside,a fairly long strip of area between the bottom of the rib cage and the genitals. With the dog comfortably settled in bed, I spend a few minutes giving him his favorite chest and belly rub. This usually causes him to relax more; in the process he rolls over and exposes the target area, where I gently hold the Zapper in place. He doesn't seem to mind the Zapping sensation. Hulda was right, within a day or two he got quite accustomed to the taste of the parsley drops added to his water, likewise with the drops of Black Waltnut Hall tincture added to his food.