In this work, we tested a setup of X-ray fluorescence (XRF) excited by proton-induced quasi-monochromatic X-rays (proton-induced XRF (PIXRF)) as a low-radiation dose analytical technique for precious cultural heritage samples. The low-dose performance of the PIXRF is experimentally assessed in comparison with the performance of a conventional XRF. For this assessment, we prepared test samples, which simulated original Japanese paintings with copper-bearing pigments. By introducing a figure-of-merit, the PIXRF is found to potentially give a better performance in terms of the radiation dose to the sample and the limit of detection, albeit the degraded multi-elemental analytical capability. PIXRF can be a cost-effective method to perform low dose measurements of precious samples, if introduced in an existing PIXE facility.