Multi-MeV proton beams can be generated by irradiating thin solid foils with ultra-intense (>1018 W/cm2) short laser pulses. Several of their characteristics, such as high bunch charge and short pulse duration, make them a complementary alternative to conventional radio frequency-based accelerators. A potential material science application is the chemical analysis of cultural heritage (CH) artifacts. The complete chemistry of the bulk material (ceramics, metals) can be retrieved through sophisticated nuclear techniques such as particle-induced X-ray emission (PIXE). Recently, the use of laser-generated proton beams was introduced as diagnostics in material science (laser-PIXE or laser-driven PIXE): Coupling laser-generated proton sources to conventional beam steering devices successfully enhances the capture and transport of the laser-accelerated beam. This leads to a reduction of the high divergence and broad energy spread at the source. The design of our hybrid beamline is composed of an energy selector, followed by permanent quadrupole magnets aiming for better control and manipulation of the final proton beam parameters. This allows tailoring both, mean proton energy and spot sizes, yet keeping the system compact. We performed a theoretical study optimizing a beamline for laser-PIXE applications. Our design enables monochromatizing the beam and shaping its final spot size. We obtain spot sizes ranging between a fraction of mm up to cm scale at a fraction of nC proton charge per shot. These results pave the way for a versatile and tunable laser-PIXE at a multi-Hz repetition rate using modern commercially available laser systems.