The inner tubes wouldn't have enough elasticity in them to work effectively.
So here is where I got my surgical tubing for my team. This is out of the U. of Michigan:
http://www.lanegainer.com/catalog.htm Scroll all the way down and you can buy tubing in feet. I believe the more expensive the more resistance and don't go any lower than red. You can buy the paddles on this site or you can cut the tubing and tie it in knots to make loops to fit your hand in.
The knots will come loose over time so I reinforce mine with those plastic ties that I can't recall the name of. They are the ties you can buy in the hardware store that you can tighten but can never loosen. In fact, I think they've always come with my bike computer to fasten the wiring to the bike frame.
Hope that makes sense.