I volunteer with Max's Pet Connection and we don't require a fence. Actually we would prefer that the dog NOT be left in a yard by itself (at least the medium/small dogs) due to potential predators taking the dog.
We don't have any purebred Yorkies right now, and only get them rarely. Hypoallergenic purebred dogs are always in high demand, so you may have a long wait unless you go to a breeder. If you are not locked on a purebred, we do have several Yorkie mixes. One in particular is Romeo, who is a Yorkie/Maltese mix. Frankly I am surprised we still have him-he is such a sweet dog.
Here is a link to the adoptable dogs web page for Max's Pet Connection:
Link You can scroll through the different dogs-but if you click on a dog and don't see information, please scroll to the top of the web page and you will see some additional information. Max's Pet Connection has the fosters bring their dogs to PetSmart on 441 in Lady Lake almost every Saturday from 10-2.