Salt is a binder, and if you let the sausage sit too long it will get "stiff". As byacery stated; mix the cure in the water that you are adding to the sausage mixture, and mix well. I mix until I get that primary bind; when the mixture becomes a sticky mass. You can continue to mix at that point, but I find it is not needed. There shouldn't be a problem with dispersal of the cure. Since the cure is mixed into the meat, the cure starts to work immediately, so you can immediately stuff, and take the sausage to the smoker. In addition if you are smoking it, the low heat during the drying and smoking times, accelerates the curing action.
When I smoke sausage, I will always stuff right away. Then because most of the daylight time is gone, I will refrigerate overnight and smoke them the next day. I rarely have a problem with the meat separating from the casing. Those times that it has separated was due to improper stuffing.