NiTi shape memory wires are widely used in several markets, mainly for medical and aerospace applications, due to their excellent properties including superelasticity and shape memory effect. The combination of NiTi alloys with other alloys can provide high flexibility in the design of various smart structures. Nevertheless, the joining of NiTi alloys is really challenging because of the effect of thermal history on the functionality of welded joints. In fact, the temperature can change the microstructure and the balance of the material composition in the welding area, and, consequently, it leads to some alterations in the transformation temperature of the welded zone. The present study reports the effect of laser parameters, namely, laser power and scan speed, on the functionality of laser-welded NiTi to NiTiCu wires. The experimental findings allowed us to identify the best operational windows of the laser parameters, stating welding by high-power diode laser as an extremely promising technique in joining of dissimilar NiTi wires.