I used 'sweating tin hats' today, after a spring fever bout of hoovering. It was something my father used to say which places its usage in the English West Midlands in the first half of the 20th century. Thinking back now, I recall that it was used to express anxiety not perspiration and expect that it was a polite version of 'shitting...'. The tin hats were 'tommy atkins' army helmets.
In the playground we also used 'shitting/sweating blue bricks' (that region is built on a band of blue clay which was made into the local brick).
I've also heard 'sweating cob nuts'. I'm guessing that other regions may had had their own versions of 'sweating/shitting...' one thing or another. Any others?