.....not exactly slings w/o pouches, but maybe a possibility. The photo below shows 2 pouches I made out of simple strip material.
The black one is just 2 strips of leather measuring 1" x 7" punched at each end, then crossed over before being attached to the cords. It's the crossover that makes a nice slightly cupped pocket.
The spiffy red one is a 15" long strip of 1"wide woven strapping material. twisted 360deg, then ends lapped over 3/4" and sewn securely to make a loop. More stitching makes "tubes" at the ends of the loop to run cords thru. The 360deg twist makes the loop cross over in the middle, and that creates the nice slightly cupped pocket as before.
It's not hard to imagine a sling made entirely of a single strip of material (about 12ft long), doubled over on itself to make the cords, and crossed over in the center like these to make a pocket. A long leather strip could even be shaped along it's length to keep the cords narrow while providing an ample pocket.
FYI, the pockets shown are combined with 1/8" braided nylon cord to create a pair of 35" slings. They work quite well!
Maybe the answer to how Ulrica gets her all leather sling, made out of just one piece of leather. mgreenfield