"You may need to re-cover it" they advised. What a fab idea.
So I bought some music notes fabric from Amazon (about £6.50 for twice what I needed).
Then I cut the fabric in half.
I unscrewed the padded seat from the main body of the stool
I stapled the fabric onto the seat.
I screwed it back on to the stool
And here are the boys, performing a stool test (I had to get that gag in somewhere...)