Green’s Dictionary of Slang

skidoo n.

1. bad luck [SE skid].

1906		‘Hugh McHugh’ Skidoo! 10: Skiddoo for yours!
1913		J. London Valley of the Moon (1914) 174: You’re a bonehead. A plug. [...] Skiddoo for you. Skiddoo for all of us.
1915		Wodehouse Psmith Journalist (1993) 302: It’s a real skiddoo, is a cat wit one blue eye and one yaller one. Puts you in bad.
1942		E. Ferber ‘Grandma Isn’t Playing’ in One Basket (1947) 546: This would have sounded as dated and ineffectual as the ‘nit,’ ‘rubberneck,’ ‘skiddoo’ of a still earlier day.

2. an exit [skidoo v.].

1906		‘Hugh McHugh’ Skidoo! 94: He thinks he has Shakespeare on a hot skiddoo for the sand dunes.
1908		K. McGaffey Sorrows of a Show Girl Ch. ii: ‘No knocking or nothing; just sit and talk real friendly like.’ ‘That’s the idea and if anyone starts the anvil chorus they get the skiddo.’.
1911		‘Sing Sing No. 57,700’ My View on Books in N.Y. Times Mag. 30 Apr. 5/6: Some of the wise ones tout W.D. [Howells] as a winner, but there’s nothing going for me. Skidoo for him.
1914		Manchester Courier 18 Apr. 8/5: If I hadn’t taken it I should have done a skidoo quick.
1957		D. Niland Call Me When the Cross Turns Over (1958) 186: So ... forty fights, forty wins, and skidoo, out.

In compounds

skidoo hat (n.)

a protective helmet.

1906

Int’l Gaz. (Black Rock, NY) 29 Sept. 8/3: Bartz, Spitz, Tackhead, Woodenleg [...] all wearing skidoo hats.