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I saw an "antenna" (felt inclined to specify) that was 3.5" but I never found where you could buy one like it? in this case, the shorter the better imo, as long as it works.
Hmmm, 4.5" grinder with a cut off wheel, a touch of black spray paint and a artist brush. Just removed my antenna and eyeballed my length. Cut it with the grinder and hit the brush with a touch of paint and applied to the cut. Reinstall antenna, done. Cost me nothing but 5 minutes. Don't need the ball but a $.05 vacumme cap would work nice too.