I wear the cornuto sign, in the form of a small gold pendant all the time. It's suspended from a gold chain, so it really can't be seen. But, in the event that it is seen by someone - most likely during summer wear, with an open shirt, and over my T-shirt - I'll give them one of two stories about it. If it's someone I feel comfortable enough with to tell them its true meaning for me, and about the lifestyle, I'll do just that. On the other hand, if it's someone I don't wish to share all of that with, I'll give them the alternate story.
The other purpose of the cornuto sign is to protect against the "evil eye", which is sometimes directed at a man's genitals. From what I've found, this is most prevalent in Italian culture. So, if I don't want to share too much about myself, this is the story I'll tell. I'll also add that it's really just a novelty item for me.