Fred,
I would suggest that you try the Code Zero Torque Line that Yale makes, the stuff doesn't twist but is pretty flexible. I think it should be able to do what you need and work well. Look at this link to Yale, page 12 on the Adobe file, page 10 of the catalog
HTML Code:
http://www.yalecordage.com/html/pdf/YaleCatalog-pleasure.pdf
I might try that line, but perhaps someone else here has a suggestion ?
Brian