OED : for "willy-nilly" : haphazardly, at random, existing or occurring whether one likes it or not also for plain "willy" : well-disposed, benevolent. Also, In NW Australia - willy is a cyclone or dust storm.

While looking that up I ran across another interesting word : "willyart" = wild, shy, self-willed, obstinate.

And plain old willy is given as : willing, eager, -OR - a sudden squall in the south Pacific!

Ain't dictionaries wunnerfull ?

No mention of course, in the staid Oxford English, of "willy" as a euphemism for a man's dangly bit!