To me, a prissy person is someone who is rather cissy, fussy and stuck up. So I do see the nickname as having negative connotations. If I heard someone call a boy that name, I'd assume they were teasing him (even if they meant no real nastiness by it).
I realise that your family is doing this in a loving, private way, but as a PP said, all it takes is one slip of the tongue to make the nickname public. I remember as a kid reminding my mum over and over not to call me [Silly Family Nickname] in front of my friends. Unfortunately, she'd inevitably forget, and I'd cop some teasing from the other kids! So it can happen easily.