I think, perhaps, you were just looking for a lighter alternative, OP. I know what you mean.
All 3 of my boys always loved shorts at school - cooler, no material to rub against legs, bit roomier (esp with one's with combat pockets on the side they got when a bit older primary). I always loved them with short-sleeved school shirt, tie & tanktop and/ or blazer- so smart. DS1 loved them so much it was a struggle to get him out of them when it turned colder, & he moaned so much that he wasn't allowed at secondary school 😆. Older 2 played/ play rugby, so I suppose shorts were what they were used to all the time, so seemed more normal & less formal than trousers.
Maybe you'll grow to like them. M&S do grey ones that are pure cotton, so they might suit?
My friehd in Canada's kids- even in secondary- had school tracksuit/ polo/ shorts made of sweatshirt. All the same so could hand down to either sex. Sensible!