In my experience, it's not the spurs that are a problem to the hens, as much as the toenails. Just blunt the toenails with a file, or I use a dremel. The pet dremel is inexpensive, and does a great job at blunting toenails, and spurs.
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She is screaming because she is not cooperating with him and the fact that he is chasing her also tells you that she is not willing.... that is likely to lead to injury. He will grab her and she will pull away.... that is how feather loss happens. He needs to stand on her back to mate her and hold onto the back of her neck to balance himself. She is supposed to squat with her wings wide to balance herself so that she creates a steady platform to support his weight. If she is struggling, he can easily slip and gash her.