Green’s Dictionary of Slang

stook n.

also stock, stoock, stookey, stouck, stuke
[? Ger. Stück, a piece of cloth]

a pocket handkerchief.

[US]‘Jonathan Slick’ High Life in N.Y. I 4: There was a chap [...] with the edge of his dickey turned over his stock—like an old-fashioned baby’s bib.
Bolton Chron. 26 Sept. 8/3: According to this slang, [...] a handkerchief ‘ billy,’ ‘ fogle,’ ‘ stuke,’ or a ‘ wipe,’ &c.’.
[UK]Hotten Dict. of Modern Sl. etc. 103: STOOK, a pocket-handkerchief.
[US]Matsell Vocabulum 87: stuke A handkerchief.
see stook hauler below.
[UK]Leaves from Diary of Celebrated Burglar 13/1: I observed the same, seedy looking fellow [...] drawing a ‘stuke’ from the ‘bloke’s’ tail. [Ibid.] 74/1: The latter of whom, upon seeing me, drew his ‘stook’ from his coat ‘kick,’ and holding it close on the nasal department, cried out [etc.]. [Ibid.] 74/2: On the mantlepiece [...] a few penny pictures and ‘bawbee stookeys’ intermixed with snarls of thread.
[UK]Sl. Dict.
[Scot]Dundee Courier 12 Feb. 7/6: Here, youngster, let’s see how you filch a stook.
[UK]P.H. Emerson Signor Lippo 48: All I get is my kip and a clean mill tog, a pair of pollies and a stoock, and what few medazas I can make out of the lodgers and needies.
[Aus]Truth (Sydney) 28 Apr. 3/3: Brushing a speck of dirt off his tan boots with his scarlet silk stuke.
[Aus]Crowe Aus. Sl. Dict. 81: Stook, a pocket handkerchief.
[Aus]Sydney Sportsman (Surry Hills, NSW) 7 Nov. 1/1: Kelly had a ‘black boy with a white handkerchief’ stationed in the top corner of the grand stand [...] The presence of the black boy and the white stook [...] stiffened the pony.
[UK]Wkly Mail (Cardiff) 12 Sept. 2/6: ‘I had the guv’nor’s brown boots and a red ‘stuke’ which I sold to a chap for a ‘tanner.’ Mr. Jackson (clerk): What is a stuke? Detective Scrimshaw: That is slang for a silk handkerchief .
[Aus]Bulletin (Sydney) 2 Sept. 26/1: What gave me the rift in the gizzard was that one of the mob booted the carpet off me arf-a-quid lid, and another potted a new stook and four jim that I was goin’ to weigh out for me new clobber.
[UK](con. 1900–30) A. Harding in Samuel East End Und. 284: Stook/stuke – A silk handkerchief.

In compounds

stook buzzing (n.) [buzzing n.1 ]

(UK Und.) pickpocketing handkerchiefs; thus stook buzzer.

[UK]Bell’s New Wkly Messenger 9 Mar. 6/2: The buzzer, or gentleman’s pickpocket, is either the stook buzzer [...] purloiner of pocket handkerchieves, or the tail-buzzer, seeking [...] sneezers (snuff boxes, or skins and dummies (purses and pocket books).
[UK]Leaves from Diary of Celebrated Burglar 55/2: Soon he and the eldest of the two commenced partnership in the ‘stook-buzzing’ line, and from that to ‘tail-dipping’ for a ‘skin or dummy’.
[UK]Exeter Flying Post 20 Apr. 6/6: Stook-Buzzing or ‘Fogle-hunting’ [...] is followed onl by boys who band together, one being the bagman, the sxecond the stall, while the third [...] keeps a look out [...] is called the swagsman, it being the chief part of his business to carry or ‘swag’ the ‘stooks’ or [...] ‘fogles’.
stook hauler (n.) (also stook buzzer, stock buzzer, stuke buzzer) [buzzer n.1 (1)]

(UK Und.) a thief specializing in taking pocket handkerchiefs.

[UK]Hotten Dict. of Modern Sl. etc. 103: STOOK HAULER, or buzzer, a thief who takes pocket-handkerchiefs, thus stook-hauling.
[UK]H. Mayhew London Labour and London Poor IV 25: those who plunder by manual dexterity, by stealth, or by breach of trust [...] ‘Stook-buzzers,’ those who steal handkerchiefs. [Ibid.] 303/1: The pickpockets in lodging-houses, for the most part, are stock-buzzers, i.e. stealers of handkerchiefs.
[UK]Birmingham Dly Post 26 Dec. 3/4: ‘We did a little in “stoucking-hauling” line (pocket handkerchief stealing) but soon found that “stoucks” don’t fetch above threepence’’.
[UK]Leaves from Diary of Celebrated Burglar 13/1: We [...] got to the entrance in time to see the ‘stuke buzzer’ hauled off to the ‘booby hatch’.
[UK]Sl. Dict.
[Aus]Sydney Sl. Dict. (2 edn) 8: Stook Buzzers - Handkerchief pickpockets.