Merriam Webster
Main Entry: wog
Pronunciation: 'wäg, 'wog
Function: noun
Etymology: perhaps short for golliwog
Date: circa 1929
chiefly British, usually disparaging : a dark-skinned foreigner; especially : one from the Middle East or Far East
Word Reference.com
wog1 [wɒg]
noun (British) (slang) (derogatory)
a foreigner, esp. one who is not White [ETYMOLOGY: probably from golliwog]
Your Dictionary.com
wog
n. Chiefly British Offensive Slang
Used as a disparaging term for a person of color, especially a person from northern Africa or western or southern Asia.
Dictionary.com- lists a similar definition.
wog - World War II British armed forces slang for "native of India" (especially as a servant or laborer), possibly shortened from golliwog.
http://rec-puzzles.org/sol.pl/language/english/etymology/acronym
Supposed (but not real) acronyms:
wog Worthy (Wealthy) Oriental Gentleman
NOUN: Chiefly British Offensive Slang Used as a disparaging term for a person of color, especially a person from northern Africa or western or southern Asia.
ETYMOLOGY: Probably short for golliwog.
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Which would bring us to golliwog: (again the American Heritage Dictionary)
NOUN: A doll fashioned in grotesque caricature of a Black male.
ETYMOLOGY: After Golliwog, a character in books by Florence Upton (died 1922), American illustrator.
Some more info on the etymology of the word wog and offered by Oxford's
http://acadprojwww.wlu.edu/vol4/BlackmerH/public_html/xliberty/oed/wogcite.html
All Personel, South East Asia Theater of War: Upon receipt and thereafter, you will cease refering to our allies as slopes, gooks, slants and yellow bastards and afford them the respect due to the worthy oriental gentlemen that they are.
Viscount Robert Mountbatten Commanding General South East Asia
While no etymologist I, it would seem from your research that Mountbatten was engaging in some particularly Churchillian word play.
Surprising, though, was your unfamiliarity with the term. Robert Ruark built two African novels on it; Uhuru and Something of Value. If you have not read either or both of these you, in particular, should not eat nor sleep until you have copies. It will be worth your while.
One of the original Upton "Golliwogg" illustrations:
And one of the many subsequent incarnations of the craze:
As one source points out, the doll in the story was copied from blackface minstrel show costumes, making it a caricature of a caricature...