I wouldn't refreeze it if I were going to eat it. It looses too much of the moisture when it thaws. For the dogs, I do it all the time and have never had any bad results from it.
Are the ducks all in one package or are they individually packaged but sold as 4 ducks? If that's the case just thaw one and feed it till it's gone, it will only last a couple days with your dog.