Joonam, seems that for copper dragging isn't applicable for so thin dimensoins.
In principle you can etchdown thin electrical copper wire of 50 um or 80 um. If you take varnished wire you have to preliminary remove lackuer by dissolving in HF acid, that does not attack copper. After that use dilute HNO3 to controllable etch Cu.
Another idea to dissolve electrolytically in CuSO4 electrolyte when the naked seeding wire placed in the center as anode, and cylindrical copper electrode acts as cathode.
But it seems to me that so high aspect length to diameter ratio is hardly achieveable, as 1 um comparable to the grain size and some effects of grain-dependent etching, roughness or micromechanical issues appear for this macroscopic length, so bending and breaks are possible.