You're right about the 'slang' part. I haven't been able to find the latin word for vagina, but medieval doctors used the latin for 'scabbard' as a metonymy, so as not to refer to it too 'directly' :D
Here's what Wikipedia has to say about it, in the article "Latin profanity"
"The modern scientific or polite words vulva and vagina both stem from Latin, but originally they had different meanings. The word vagina is the Latin word for scabbard or sword-sheath.
Vulva (or volva) signifed the uterus. The meanings of vagina and vulva have changed by means of metaphor and metonymy, respectively."
So there, you weren't that far off!
PS/edit - I see that the Latin word for vagina has been given below me by Robert Witt! Thank you very much!
Wikipedia and some "educational leftovers" of Latin :D