I was wondering if were any mods that make it so that my character can put their weapon on his or her back

http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=4685: side or back, depending on weapon.
There are also some modded weapons that have the script attached, like http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=2991.

There are some downsides to sheathe weapons though; they tend to use the left shoulder slot very often.

Use this mod if you still want to have 2 pauldrons. It is called Dual Pauldrons

http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=5484

Weapon Sheathe Ultimate uses the Shirt slot.... (I think)
So if you have armor on, you won't even notice. It is also easy to change it so that it uses the slot of your choice.