I would strongly recommend using line that does strech for tiring down an aircraft. It allows shock from a gust to be absorbed by the line instead of transferring all the shock to the aircraft structure. Use good quality (not cheap) nylon line, not nylon and mixed fibers also learn a few basic knots. A bowline is essential and while many people use a rolling hitch which supposedly locks on a line, they can slip. I tie my knots at the tie down so they can't slip. If the line is long, I may tie my bowline at the wing and half hitches at the ground so the long unused line is on the ground and won't beat on the plane in a strong wind.
Cubs have had failures of the lift strut attach fittings that connect the lift struts to the spars. Both fatal and non fatal. Those who use chain, or even ratchet straps are asking for trouble. One such failure on the Alaska Penninsula in the late eighties or early nineties prompted ATLEE to make two STC's, an insert that went inside the lift strut attach fitting on a cub and a tie down that went arround the spar outboard of the lift strut attach fitting thereby not involving the strut attach fitting in the tie down. I have a seat belt strap arround the spar instead of the Dodge tie down on one of my Cubs. That strut attach fitting is made to take a load in tension but when used as a tiedown the load is no longer in the direction which it was designed for and in the direction where the strength is. There is a service bulliten concerning the inspection of the lift strut attach fitting.
i do carry a realitively long piece of small diameter winch line. Sounds like it is similiar to this specter. I use this to tie to a tie down like a tree or something that is a distance away, and then tie my tiedown line to it. It is light, strong and has no strech and should only be used as a tie down line as a very last resort.