I don't think the word puca is used independently from this expression because at first sight we don't even know excatly what it is really. (You mention "his/her" before the "xxx" is a sign... Is it the male or the female sex organ? Or either?)
I looked it up and found that puca means penis. (Here is a short linguistic explanation about its origin.)
I have to admit I expected the female sex organ for it but no...
However, I also saw that in a Slav language it means "girl" so maybe this is why there has been a confusion.
To add another twist, apparently, as a Romanian originating childish term, it may refer to the sexual organ of boys or girls equally.
An article from the Kárpátalja region can be interesting because it shows that in this area (among others indicated in the article quoted above) the meaning of the word is very clear. (The saying is used exactly as we do - not only in a soldier's slang anymore).