There's a Chinese laundry man, the famous Mr. Wu
He's chucked his limehouse laundry shop and his window cleaning, too
He's got another job, and it's one of the best
Now he's doing his bit for England like the rest.

I'd call that last line definitely "an all pull together attitude in England, despite race." It's "poking fun at a foreign man" in exactly the same way as a song like "Donald where's yer troosers" pokes fun at the Scots.

Mr Wu is definitely seen as a good lad in all the Formby songs - a funny foreign lad maybe, but a good lad none the less for that, and no suggestion at all that he's a coward, let alone a traitor.