Yeah...see, I'm not real psyched about carrying around a Cheney, either. I'll have to go with the "Pain Luggage" which I find to be an apt turn of phrasing.
I don't have a separate name for the scrotum (since I like that one-- it's an onomonopeia, since that's the sound it makes!) but I have been known to refer to the scrotum's contents as "man-beans". Feel free to use that. Go nuts, as it were.