Green’s Dictionary of Slang

mushe n.

[Fr. monsieur, a term of address; Syria had been under Fr. control, and thus its expatriates might speak the language, but the link to Chinese people is unclear, perhaps on basis of all foreigners being generically ‘French’]

(W.I.) a Syrian or a Chinese.

[WI]cited in Cassidy & LePage Dict. Jam. Eng. (1980).