In the UK a wrangler is a person engaging in a lengthy and complicated dispute and a wrangle is such a dispute. The US meaning isn't common here, though people my age may remember hearing the word used to mean a person in charge of horses or other livestock on a ranch (same link) in old cowboy series on television and may therefore know why Wrangler jeans are so named.
There are no ranches here. Probably the nearest equivalent of American wranglers would be the agisters of the New Forest, who round up the semi-wild ponies from time to time.
It's hard to predict how quickly your own meanings of the word - someone who gathers, tames, subdues, organizes - would catch on here and replace its current disputatious meaning. In the rest of Europe, as long as jeans are known, the word may not seem too strange, though only a fairly proficient English-speaker would know its meaning, I think. For some Europeans it might be the first word they've encountered starting with wr.