As a result of conventional wire-forming processes, the residual stress distribution in wires is frequently unfavorable for subsequent forming processes such as bending operations. High tensile residual stresses typically occur in the near-surface region of the wires and can limit further application and processability of the semi-finished products. This paper presents an approach for tailoring the residual stress distribution by modifying the forming process, especially with regard to the die geometry and the influence of the drawing velocity as well as the wire temperature. The aim is to mitigate the near-surface tensile residual stresses induced by the drawing process. Preliminary studies have shown that modifications in the forming zone of the dies have a significant impact on the plastic strain and deformation direction, and the approach can be applied to effectively reduce the process-induced near-surface residual stress distributions without affecting the diameter of the product geometry. In this first approach, the process variant using three different drawing die geometries was established for the metastable austenitic stainless steel X5CrNi18-10 (1.4301) using slow (20 mm/s) and fast (2000 mm/s) drawing velocities. The residual stress depth distributions were determined by means of incremental hole drilling. Complementary X-ray stress analysis was carried out to analyze the phase-specific residual stresses since strain-induced martensitic transformations occurred close to the surface as a consequence of the shear deformation and the frictional loading. This paper describes the setup of the drawing tools as well as the results of the experimental tests.