In the UK there aren't really this sort of thing though when I was an army cadet we had one called something like "The lady in red" basically it lists lots of different ladies in lots of different colours but each one has a problem, usually along sexual lines.
One example is that the lady in pink/ is sure to make your finger stink.

Not sure if that was an export to us though and Im struggling to remember the words if I'm honest.

When I was around 14 I remember this marching cadence from when we marched distance:
Left, right. Your wrong it's not Right it's Left, and you'll find it: Left right where you left it. That's Right.

Maybe we just got some slack cause we were kids. But the remark about the C/Sgt is true. I remember when somebody suggested it to our corp. His reply was along the lines of "If we all started shouting as we marched along what would be the point in wearing DPM (camo) we might aswell just wear orange coveralls!. When we march distance we don't want every commie in the damn eastern bloc to know that we are coming do we!"