In my experience, stopping sweating during my rides would be about as easy as stopping breathing. If we didn't sweat at all, wouldn't we need to pant like dogs to maintain a steady body temperature? That being said, I have several thinner work colleagues who do not sweat nearly as much as I do during rides, however the OP is already fairly thin.
I would suggest that dressing as light as possible and wearing moisture wicking clothing (I like wool micro-weave) are perhaps essential steps to managing moisture. Slowing down the tempo would certainly help as well.
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Work is the curse of the drinking classes - Oscar Wilde