What an interesting thread. I heard this song from my grandfather, though never was sure if he picked it up during the war or as a schoolboy in London.

Unfortunately he used different verses that I don't see here.
There was one about 'combed his hair with a knife and fork' or something to that effect. The first verse ended with 'couldn't walk or talk' with 'talk' rhyming perfectly with short because of his accent.

The only verse I remember, which I always thought was the best, was the last one which I don't see here:

"They took him up in an aeroplane
And told him not too bash his brain
The word was said and he fell on his head
and that was the end of the Chineseman"

As far as the concerns on the board about the racist nature of this song goes, I don't think there is any risk that teaching this song will promote racist attitudes. It's just a fun look into the attitudes that prevailed back then.
Case in point: I heard that song all the time growing up, but it didn't stop me from learning Chinese, spending time in China, having Chinese friends, and dating Chinese women. It's a fantastic culture, that I greatly admire, but that doesn't prevent me from enjoying this ridiculous song.