UrW uses the "first" item of "equal" quality for a job, so if you shift the knives in your inventory (e.g. by dropping and picking up) I'd expect the broad knife to be used for skinning and the hunting knife for butchering, i.e. a broad knife is the preferred tool for skinning, while butchering only cares for knife quality, but not type (possibly with the exception of a stone knife, which may be deemed unsuitable for the task, and tends to be of a horrible quality anyway).
I suspect a hunting knife is a better weapon than a broad knife (although I wouldn't chose to use a knife for fighting).
It can also be noted that the Fishing Knife has no preferred use at all currently (it would presumably be used for cleaning fish, but that task is currently abstracted away in the game, which sort of results in the lack of fish cuts).