Harry Roy sings "My Girl's Pussy", from 1931:
https://www.youtube.com/watch?v=-_-U4oTTmQc
And be sure to check out the list of other suggestive songs down the right side.
Please Warm My Weiner
Lick It Before You Stick It
And more... Oh my!
They'll say that over the radio in many situations, whether true or not, just so that they have ready-made cover on tape in case they end up having to shoot. Other favorite phrases are things like "he's making furtive movements".