Green’s Dictionary of Slang

shin v.¹

(US) to borrow money; thus shinning n.

1834		A. Greene Perils of Pearl Street 161: To be sure, we were obliged to shin it a little now and then, as who has not? Show me a merchant of a year’s standing, who has never shinned it, and I will engage to show you a rare animal.
1842		Wkly Rake (NY) 30 July n.p.: wants to knowWho the ‘man with mysterious eyes’ [...] is, and whether he lives by ‘shinning’.
1845		N.Y. Commercial Advertiser 13 Dec. n.p.: The Senator was shinning around, to get gold for the rascally bank-rags, which he was obliged to take [DA].
1853		La Crosse Democrat 6 Dec. 2/6: Shinning [is] on the decline. [...] Stocks are rising [DA].
1872		Schele De Vere Americanisms 632: In financial slang, Americans use the verb to shin simply, where the English use to break shins, to denote a desperate effort to procure money in an emergency by running about to friends and acquaintances.
1876		Manchester Courier 16 Aug. 3/1: The Dead-Beat Nuisance [...] We have dead-beats [...] who ‘shin’ from day to day [...] Whether we call this organised beggary, or organised robbery [etc.] .
1890		Congressional Record 18 Sept. 10188/2: They find a difficulty in shinning around to borrow money [DA].

In phrases

shin out (v.)

to pay up (one’s share, one’s debts).

1889–90

Barrère & Leland Dict. of Sl., Jargon and Cant.