PTFE tubing would work pretty well, wouldn't it? The size could get trimmed down, too. Then again, you'll still have a metal ball or disk on either end. Are orthodontic braces generally made from stainless steel (I would imagine they are)?
I'm not an expert on this, but according to http://www.azom.com/details.asp?articleID=1177 :
(credit: Azom.com, http://www.azom.com/work/ycdTWC2o7CJUrDMpADF3_files/image003.gif)
Three conditions must be met for galvanic corrosion to occur:
1. the two metals must be electrically connected to each other
2. their surfaces must be bridge via an electrically conducive liquid
3. they must be "widely separated" on the galvanic series (above)
The first two are certainly true. The third, however, I'm not so sure about. If things haven't changed much, 316L and close derivatives are still used in the manufacturing of piercing jewelry. If you can find out what type specific type of metal is used in braces, we'd have a better idea. A quick google search simply turned up "stainless steel".