In this study, a method for determining the shape of arbitrary nanotubes/nanoelements from electromagnetic wave scattering profiles is developed on the basis of an IsoGeometric Analysis Boundary Element Method (IGABEM) solver that has been previously introduced in [1]. The scattering profiles are produced by a single or multiple ambient sources of light. A methodology for enabling precise identification of the shape of nanoscale structures is a key issue in various applications in nanotechnology and materials science as well as various other applications beyond the nanoscale. We mainly aim in establishing a framework that can reliably determine the nanostructure's shape and/or other characteristics, such as material properties, i.e., electric conductivity, and its position with respect to the light sources. To achieve this objective, an optimization framework was developed that uses: (i) a hybrid approach combining global optimizers with gradient-based local algorithms, for accurately determining the shape at the final stages, (ii) a series of parametric models generating valid non-self-intersecting nanotube shapes, and (iii) the abovementioned IGABEM solver which can approximate the value of the electric field with high accuracy. The inverse problems considered in this work include the following cases: (i) unknown shape with known integral characteristics, such as area or circumference, and material properties (electric surface conductivity), (ii) unknown electric surface conductivity, (iii) unknown position of the light source signal, (iv) unknown shape with known material properties, but no information on integral geometric characteristics, and finally, (v) unknown shape, material properties and integral geometric characteristics. Our results in all tested cases demonstrate a very promising potential in the the proposed methodology, yielding successful and accurate approximations for a large range of examples. Further future steps include scaling up the current implementation so that it can handle arbitrarily complex shapes as well as modifying the operational characteristics so that the proposed methodology can be applied in meso and macroscale applications, such as non-intrusive inspections and military radar applications. [1] K. V. Kostas, C. Valagiannopoulos, Optimally shaped nanotubes for field concentration, Engineering Analysis with Boundary Elements (2024), Vol. 169, Part~B