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That will work as long as it is 3/32 in size. Make sure that you use copper stops and then have them crimped small enough so they fit in the end of the last link. When I tension the cables up, I try to get them so that the chain rolls up 3/4 of the length when I crimp the other end.
The only things i need now to get it rebuilt is the copper cable stops, i have looked in every hardware store plus the local Wally mart and Canadian Tire store and no luck, i may have to order them and put the project on hold.