Green’s Dictionary of Slang

daily expenses, petty cash rather than a large amount that needs investing or depositing.

1938		D. Runyon ‘A Job for the Macarone’ in Runyon on Broadway (1954) 693: Pick up a few dibs [...] for walk-about money.
1944		D. Runyon Runyon à la Carte 24: I stake him to walk-about money, which is money for his pocket.
2012		G. Pelecanos (con. 1972) What It Was 131: There ain’t nothin here of value to speak of [...] Walkin-around money is all I got.