It is the head and down the front and legs that has the smell. Even just removing the males feed tub, means my hands are covered in billy smell. But having three intact males, and the young ones just starting to smell, I am well used to the smell, and it does not bother me now. It bothers my husband, who does not get involved with the animals, and he is always complaining he can smell goat|!!
I used to keep my intact goat at the side of the lane, in a stable, so passers by and the people in the barn opposite must have smelt him when the wind blew that way, but no one said anything. I find the smell wanes as the breeding season goes on if that's any consolation.
On the days I work, I am very careful not to touch the males - and get changed, but it does still linger!!