It’s fine.
If the dogs are overweight then white is better because it is leaner, the same rationale for humans.
But if your dogs are at an appropriate weight then I don’t see any reason not to give it to them.
When I was a child my cousin had a dog who would get loose stools from eating dark chicken meat so if one of the dogs is having this problem, try going with just white meat and see if it corrects.
That was the only dog I have ever known who had an issue with dark meat so I would say it’s rare.
Frankly, though, if you are feeding good quality dog food you shouldn’t have to supplement it with shredded chicken.
If you are doing it just to please the dogs and want to stop (and honestly if I were going to slow cook a whole chicken it would be for the humans, not the dog), try cutting back on the amounts until eventually they are just eating the dog food.
I hope that was helpful.

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