Similar to the method Tigame posted. I don't have video, but it's easy to verify.

Simply mash B and R simultaneously and Link will start to sprint, pull out his weapon as if to throw it, put it back, and then repeat the cycle with no loss in stamina.

It takes some practice to avoid making Link actually start to aim his throw. If this happens, just try pressing B slightly before you press R.

It may look like Link's animation is slower than actually just sprinting, but I've tested many splits across distances and there's no discernible speed loss.

It's also slower than whistle sprinting sadly and stamina recovers slower during it.

From what I've tried it also seems to be more or less effective depending on the type of weapon you currently have equipped (heavy vs sword) since the animation is different, but maybe I'm just bad at it.