It takes a certain type of dog to be used for shooting.
The same type of dog will not be getting cut with a catch dog either
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Probably going to jinx myself here... I cannot remember the last time one of my bay dogs was cut. As a rule, my bay dogs bay, and my catch dogs catch. (Mandi's Lizzie dog is the exception, for some reason she likes a little pain). It may help that we use two catch dogs, so even if a cur dog decides it wants to help out, they are caught on a hind leg, or an elbow. The hog is not able to get to them.
I see the merits in both ways of hunting, but I don't think it is possible to say one method of dispatching the hog (shooting vs catch and stick/tie) is safer for the bay dogs.