Aggressive Neighbor Cat

At least I think it's a neighbor cat. I guess it's possible it's a stray, but I suspect it has an owner. Anyway, we have a black cat that has been repeatedly attacking our cats. Once he(?) ripped the entire muscle off one of our cat's legs, resulting in a hefty emergency vet bill and a very long recovery. Our cats have been attacked at least three times since then, with other spats in between. He's now so bold he'll come right up to the house, where our cats hang out, just to pick a fight with them. The black cat runs away when it sees us, but still dares to regularly come around.

Obviously we could keep our cats inside, but I much prefer trying to solve the problem somehow with the black cat. We're relatively new to the neighborhood, however, and don't even know any of our neighbors, let alone whose cat it is. So we'd feel odd introducing ourselves to neighbors only to condemn their cat. Our vet suggested we trap it and turn it in to the humane society, telling them it's an aggressive stray that keeps attacking our cats. Then it would either be reclaimed by its owners and the problem would be known to them, or it would be adopted out to a new neighborhood. Yeah right: it would probably be put to sleep, as I doubt people would be interested in adopting an agressive cat. So we have a dilemma. One thing I've thought about trying is trapping it and determining if it's an intact male. Perhaps I could get it fixed and it would calm down a bit? That would be a gamble, but the best option I can think of so far. Tomorrow I plan on calling the humane society to see what advice they have. I haven't done anything yet, but I'd appreciate any thoughts or advice anyone can give.