So, did the old mylar J-discs have a seam in the mylar? Was it cut so it would form a shallow cone, or just stretched a bit to form the cone? I guess my only concern is that cuben is anisotropic, while mylar alone is (much closer to) isotropic, depending on the degree of biaxial orientation in the film. It might be easier to get the plain mylar tight as a drum with the hair dryer for this reason. Cuben can be shrunk with heat, but not predictably like plain mylar. I've found that cuben wrinkles and deforms in crazy, unexpected ways when it contracts at high temperatures. You might find it very frustrating to get and maintain a smooth, low drag surface with cuben.
Also, on a small scale, cuben has a wavy surface due to the fibers, whereas mylar is very smooth, although this is not likely to make any difference in drag that you could detect.