Green’s Dictionary of Slang

dry shave n.

In phrases

give someone a dry shave (v.) [dry shave v.¹ ]

(US) to defraud, to hoax.

1972

(con. 1930s) N. Algren ‘The Last Carousel’ Texas Stories (1995) 139: It’s how we move the minches ’n give the rubes dry shaves.