I do add fat plus the skin of the chicken. Some recipes call for 3.5 lbs. of meat, plus 1.5 lbs. of fat (combination of chicken skin and pork fat). I use a formula of 4 lbs. of dark meat, plus 1 lb. of a combination of chicken skin and pork fat. I break that combination down to .5 lb. of skin plus .5 lb. pork fat. When you grind the skin, make sure that it is almost frozen, and I also like to chop the skin up before running it through the grinder. I've been thinking of using another substitute for pork fat, but haven't found one, as of yet. Cooked rice is one way to replace the pork fat. I have done that with some success. If you do a search for Thai Chicken Sausage, there is a recipe that uses rice to help retain moisture.
You can use white meat, but it is very lean, and can come out dry. Plus I find the dark meat not only more moist, but also more flavorful.