Green’s Dictionary of Slang

(US black) a motor vehicle.

1934		J. O’Hara ‘Back in New Haven’ in New Yorker 6 Oct. 24/1: [T]o think of my taking her home to her house, parking her station wagon in her driveway, and driving away in my own ‘wheelchair’ at top speed.
1944		D. Burley N.Y. Amsterdam News 16 Sept. 12A: He’d just nixed out from his wheelchair, stashed by the step-off.