Actually, Shanghai had a quite sizable expat community of Caucasian people that was around 50,000 strong in the 1930s. And they had extraterritoriality treaties in place that provided especially British and American inhabitants many privileges the locals didn't have. Willie being a part of that community is not so outlandish.
Of course, this doesn't mean that they couldn't have created a character of more Oriental ethnicity in her stead. The city was quite the melting pot at the time. And even if she was white, she didn't have to be American. One curiosity of that white community was that about a half of them were
Russian, former supporters of the Czar who had fled the Communist revolution in the Motherland. And, coincidentally, many of them happened to find employment in music and entertainment. In fact, this is probably the story behind most of Willie's backup dancers... and I'm not talking about the blondes in the backstage fantasy sequence - if you look closely, very few of those dressed in the Chinese garb have strikingly Oriental features. The matchstick girl Indy accidentally punches doesn't look very Chinese either. (They were obviously struggling to find extras of Asian origin in England.)