Where I grew up is infested with them
. I think Arran is one of the places where you can still get a licence for farming them - simply because any future release wouldn't cause much difference in the scheme of things.
Once one has a taste for your chicken run keeping it way from the eggs can be a real chore and fencing becomes a necessity. They fight the cats. Actually I think cats back them into corners and end up with their faces rippied to ribbons.
The damage they've done to the bird population on some smaller islands is hefty. On the mainland they seem to spread out and don't become quite so big a problem and Arran would be somewhere inbetween, a bad case scenario rather than a disaster area.
On the whole they weren't that big a problem if they kept to the rivers. I doubt if they'd turn their nose up at crayfish so might be helping you out somewhere along the lines. Have seen them eating crabs on a couple of occasions. The population has to be pretty high before they're taking any more fish than the otters, heron, etc.
Having watched four of them systematicaly raid a nesting area on a cliff though, eating eggs, chicks and destroying much more than they really had to. I'd say go for it. The folk I knew who trapped them used box traps, solid walled, dirtied up and set on walls and logpiles where the curious mink would be inclined to duck through them.
Some folk poisoned them but poison is so indescriminate, you don't really know what's going to eat it. Out the other side of the village the farmer regularly walked the river with a shotgun. It must have made a fair improvement in the surroundings as he kept at it for years.
Have heard they can be snared but never met anyone whos done it, just heard stories of it being possible.