Can you sheathe your weapon in Borderlands 2?
Solution 1:
No. The closest you can get to putting your weapon away is completely unequipping it.
Solution 2:
I tend to equip very small weapons when I am just running around. Some weapons are so small that when you are running, they completely leave your field of view. You'll have to experiment to see what weapons work the best, but pistols and SMGs tend to be the smallest weapons in the game.