“Wild man” Andrew Ucles is perhaps best known for catching wild Australian deer bare-handed, but he performs the same feat with other animals as well, including rabbits, kangaroos, reptiles, and even a male feral goat.
Feral goats are not unlike feral pigs in that they remove scrub and vegetation essential for other species. While they might not pose a problem for much of the continental United States, feral goats are a nuisance in island ecosystems such as Hawaii, New Zealand, Great Britain, and Australia. These animals are considered an invasive species in many of the areas where they are introduced, but traditional management practices have never included wrestling.
Needless to say, do not try this unless you are a professional. Probably not even then.