How soft and flexible do you need the sheath to be? Most cordura sheaths have a stiff insert to house the blade, and aren't much more comfortable than kydex in long term wear. Plus a flexible sheath will let the blade cut through - a parachute jump qualified sheath is really just a great product liability testimonial - it can take a hard landing and not let the blade stab you.
The only flexible sheath I've used came in leather with the Gerber MKII's, and they suffered for it in the field - the blade would rock back and forth cutting them up, and they rode up on the belt punching me in the ribs. Most leather sheaths are much stiffer and do a better job.
Eliminating copolymers as a material leaves out the best example I have - the original issue Nam sheath for machetes was a heavy molded vinyl that works great.
Perhaps a description of the difficulty you're trying to overcome will open up other alternatives.
