We introduce a new method based on the transient-current technique (TCT) for the radiation tolerance assessment of an n-in-p junction with a deep n-well on a relatively low-resistivity p-type substrate commonly used for HV-CMOS pixel sensors. The transient-current method here employed uses a femtosecond laser to generate excess carriers via a two-photon-absorption (TPA) process. Special attention has been paid to overcome the limitations of the conventional transient-current method based on single-photon-absorption carrier generation when applied to the HV-CMOS sensors. Specifically, we tackle the precise determination of the depletion region boundaries, including the deep-n-well spatial location, needed to calculate the effective doping concentration of the substrate. As illustration, we have applied this new TPA-based method to both a fresh and a neutron irradiated single-pixel deep-n-well diode manufactured in a 180 nm high-voltage CMOS process. In the irradiated device, concurrent with the expected effective acceptor removal in the p-type substrate, an indication of an effective donor removal in the DNW implant was also observed.