Whilst I wholeheartedly agree with Duckwing's perspective, I also look at it from a 'keepers perspective so far as 'vermin on a shoot' is concerned.
A litter of mink will decimate a release pen overnight (I have seen it happen) and so with a need to control the animals to protect stock then this must be your primary outlook.
If the stream is nowhere near any protectable or confined game or poultry then live and let live
So far as habitat is concerned, mink with run any waterway, still or moving, and any hedgerow or rabbit bury in search of food
OTC