Would the language really be worse off if there was no such word as "genitals" - ie "the wherewithal to proceate new members of the breeding stock" - just call them yer snatch, cock and balls, yer fucking pansy!
... or even, "the organs you piss with", as in this limerick:
There once was a girl from Aberystwyth
Took grain to the mill to make grist with,
But the miller's son Jack
Laid her flat on her back
And united the organs they pissed with.