Well-known conductive molecular wires, like cumulene or polyyne, provide a model for interconnecting molecular electronics circuit. In the recent experiment, the appearance of carbon wire bridging two-dimensional electrodes -graphene sheets -was observed [PRL 102, 205501 (2009)], thus demonstrating a mechanical way of producing the cumulene. In this work, we study the structure and conductance properties of the carbon wire suspended between carbon nanotubes (CNTs) of different chiralities (zigzag and armchair), and corresponding conductance variation upon stretching. We find the geometrical structure of the carbon wire bridging CNTs similar to the experimentally observed structures in the carbon wire obtained between graphene electrodes. We show a capability to modulate the conductance by changing bridging sites between the carbon wire and CNTs without breaking the wire. Observed current modulation via cumulene wire stretching/elongation together with CNT junction stability makes it a promising candidate for mechano-switching device for molecular nanoelectronics.