This particular shape "screams" 3D printed. There are a number of programs which would allow one to create the model to be printed. I'm particularly fond of OpenSCAD, a descriptive language type of 3D modeling software, but many others have this capability. One would be able to configure for high resolution to reduce layer lines, as well as to print with ABS for acetone vapor smoothing. The model's height means that it might have to be printed in vertical segments, but ABS also solvent-welds with great strength and sands nicely. With finer abrasives (Micromesh™), a mirror finish can be achieved. (direct experience)
Once the model is printed, it can be coated with an electrically conductive paint. The resulting model can then be processed with electroforming:
Electroforming is a metal forming process in which parts are
fabricated through electrodeposition on a model, known in the industry
as a mandrel. Conductive (metallic) mandrels are treated to create a
mechanical parting layer, or are chemically passivated to limit
electroform adhesion to the mandrel and thereby allow its subsequent
separation. Non-conductive (glass, silicon, plastic) mandrels require
the deposition of a conductive layer prior to electrodeposition. Such
layers can be deposited chemically, or using vacuum deposition
techniques (e.g., gold sputtering). The outer surface of the mandrel
forms the inner surface of the form.
This process can be accomplished at the hobby level, although for something of the size described, it may be necessary to use a commercial resource. Nickel is not particularly expensive compared to silver metal and can be quite shiny.
For the option of wrapping, silver Monokote™ exists in the radio control airplane world. This allows heat shrinking to remove wrinkles and to cause the adhesive layer to activate, but there would be a joining line on the surface.
As a final option, once the model is created and the surface is smooth to a satisfactory level, a carefully applied paint job may provide the desired results.