Green’s Dictionary of Slang

(US) to curry favour.

1918		D.G. Rowse Doughboy Dope 9: Czyerznski only ducked a spell in the jug by handshaking with the top-kick due to going AWOL.
1932		J.L. Kuethe ‘Johns Hopkins Jargon’ in AS VII:5 333: handshake—v.—to curry favor.
1941		M. Hargrove See Here, Private Hargrove 56: ‘Now this Corporal Gantt, when he first came in, was one of the greenest rookies in the bunch. But he snapped out of it and made corporal in four months.’ ‘Was that soldiering...or handshaking—as the Latins used to say, mittus floppus?’ [HDAS].
1959		(con. 1940s) C. Ogburn Marauders (1960) 277: Tom’s radio operator, ‘was a real handshaking son-of-a-bitch! I’ll bet he made corporal the day they drafted him!’.
1962		(con. 1940s) G. Mandel Wax Boom 73: I ain’t hand-shaking nobody.