Surface Nanoscale Axial Photonics (SNAP) is a promising technological platform for creating novel optical devices such as compact high-Q tunable delay lines, signal processors, and optical comb generators. For this purpose, the development of simple and reliable methods for the accurate introduction of a nanometer-scale variation of the optical fiber surface is desirable. Here, we present an easy-to-implement technique for the introduction of nanoscale variations of the effective optical fiber radius by annealing with a heated metal wire. Using the proposed method, we introduce modifications of the fiber effective radius with accuracy better than 0.1 nm without post-processing, making the proposed approach the simplest alternative to the previously developed SNAP fabrication techniques.