Dander is up! Clearly an Australian is needed: the categories call for a different characterisation. I suggest...
Formal / Informal / Indirect
breast / tits, boobs / chest
vagina / vage / privates
vulva / pussy / privates
penis / dick / privates
testicles / balls / privates
scrotum / sack, balls / privates
buttocks / bum, backside / butt?
I doubt one need teach coarse varieties of the informal. All the doc need for "handling" an unexpected word is, "Sorry, your what?" and the uneducated/inbred/illbred/migrant/retard will likely wave his/her claws at or around the diseased region. The Doc may then laugh politely. "Oh yes," she may say, "Well, don't worry, I've seen w--OH MY GOD!!! What the-, Oh-, I-, Oh, no-, no, you'll definitely have to... a specialist, you'll have to see a specialist.... Yes, definitely." She can use her cell phone for the internet snap shot.
I imagine "butt" has found it's way into Australian usage, and I think "nut" always was, as in "my left nut," but should any Australian be found uttering the plural, and it's with understandable horror that I attempt to write this, why, it would be the kind of linguistic imperialism our fore fathers fought so strongly against. Does anyone remember Nobby's, a purveyor of healthful snacks, and their pleasant, family-oriented slogan, "Nibble Nobby's Nuts"? How ribald! How distasteful! How low have we sunk?