That should be fine. I do not think you need to do anything else. You might not even have to do that much.
Depending on the dog, it is sometimes safer to feed whole chickens than pieces, sometimes the other way around. Dogs who gulp their food without chewing need it small enough to gulp safely, or else large enough that they are forced to slow down and chew (I once saw "as large as the dog's head" as a guideline for how big will force the dog to chew instead of gulping it whole.) For dogs that will chew their food, you can serve whatever size pieces are convenient for you.
I would say skinning is worth doing if you want to, but it generally seems to be safe enough for a dog to eat the skin and feathers if it wants to. If you skin the cockerels, that does make it easier to dispose of the feathers neatly, rather than finding some lying around when the dog finishes eating. If you are trying to keep the dogs from making the connection of chicken = food, I do not know if skinning will help or not, but I am sure it would not hurt either.