Summary form only given. We present data from experiments using nested wire array Z-pinches where the wires of one of the arrays (outer or inner array) are inclined to produce a cone. The use of conical arrays can potentially provide a valuable tool in pulse-shaping for Z-pinch driven high yield Inertial Confinement Fusion schemes. Results from both Z and MAGPIE (18MA, 100ns and IMA, 240ns respectively) are presented and compared. Diagnostics employed to study the effect of the conical arrays on the nested implosion included laser shadowgraphy, time resolved XUV and soft x-ray emission imaging, radial optical streak photography simultaneously at multiple axial positions in the array, PCD and XRD detectors, bolometers and an axially resolved XRD (zipper) array. Results indicate that the use of a conical outer array with cylindrical inner array causes an axially-non-uniform implosion of the outer, with the region near the smaller diameter cathode leading ahead of the larger diameter anode. A uniform variation between the two electrodes produces an axial zipper. This leads to an axial dependence of the time that the imploding outer array reaches the inner array, hence elongating the interaction pulse emitted. This axial dependence seeds a zippered implosion and stagnation of the inner array, causing a temporal lengthening of the main X-ray pulse. Separate experiments show that while a conical inner array has a strong effect on the length of the interaction pulse, it has a less significant effect on the main X-ray pulse. The possible pulse-shaping capability of combining two nested conical arrays allowing independent control of the length of the two pulses was also described.