Wha Saw The 42nd? -- traditional lyrics

In elementary school we sang Wha Saw The 4nd? during music time. But this was in San Diego and the teacher was, of course, American. I don’t know if he knew the lyrics. Maybe I misunderstood them. But the lyrics I ‘remember’ are different from what I see online. For example in my teacher’s version, the 42nd were ‘marching through the brambles brah [broad]’, not ‘marching down the Broomielaw’ and ‘some of them had’ sounded like ‘zoom-de-dim-dah’. Again, maybe I misheard. But I don’t think so. I suspect that the teacher, or whoever taught him the song, had trouble with the Scottish accent and made up nonsense lyrics so American kids could sing it.

In any case the lyrics I [mis-]recall, corrected for elementary school errors, go like this:

*Wha saw the 42nd?
Wha saw them goan awa’?
Wha saw the 42nd
Marching down the Broomielaw?

Some of them hae boots and stockings
Some of them hae nane at a’
Some of them hae woolen trousers
Marching down the Broomielaw*

Some of the lyrics are the same as I see online, but may be in a different verse. But what are the traditional ‘official’ lyrics?

If this song began in a written version at all, then the way it was sung probably strayed from the print early on. Local versions or versions modified to suit the occasion would have happened, and once that happens the lyrical waters become muddied.

There might not even be any “canonical version” waiting to be found - even if one did know where to look.

ETA: I just saw on the Wikipedia page on The Black Watch that your song is a reworking of an older song called “Wha Wadna Fecht For Charlie”. That makes it even more likely that there IS no “one true version” to be found.