Green’s Dictionary of Slang

1. an imitation of a person.

1863

Story of a Lancashire Thief 9: He’d write his own songs for the races and fairs, and he wrote one once about Louis Napoleon [...] and I remember that as Joe chanted his rhymes he worked a quockerwodger that made everybody laugh like mad, for it was the best likeness of Louis you ever saw.

2. a politician acting in accordance with the instructions of an influential third party, rather than properly representing their constituents.

1860		Hotten Dict. of Modern Sl. etc. (2nd edn) 197: quockerwodger The term is used in a slang sense, to signify a pseudo-politician, one whose strings of action are pulled by somebody else. ― West.
1864		Kentish Gaz. 22 Nov. 2/5: A pseudo-politician, one whose strings of action are pulled by somebody else, is now often termed a ‘quockerwodger’.
1873		Sl. Dict.
1895		C. Crowe Aus. Sl. Dict. 64: Quockerwodger, a politician whose strings of action are drawn by some one else.
1925		Diss Exp. 10 Apr. 7/1: Doe anyone remember the Quockerwodgers of yesteryears [...] subservient politicians who did what they were told to do.
2018		Times 26 July 🌐 Putin the master controlling Trump his quockerwodger yet again.

3. used attrib.

1876

Preston Chron. 17 June 5/1: Witchcraft has become obsolete, crowds of old-world delusions and dim quockerwodger tomfooleries have floated down the stream of time.