The Camp Vibes Hybrid Shorts from Poler.
Old school vibes married to a modern fit and material make these shorts great for biking, skating, running or swimming. The fabric is nice and matte, and looks a whole lot like standard cotton. This means you won't feel like you're wearing a boardshort, but that doesn't mean you can't jump in the river on a whim.
The inseam is 6 inches, and if you're unsure about sizing go up a size rather than down. They have a drawstring at the waist along with mesh pockets and drainage grommets that water can flow through.