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This paper analyzes the impact of hybrid nanoparticles (Cu–TiO2) on a two-dimensional peristaltic blood flow pattern in a nonuniform cylindrical annulus in the presence of an external induced magnetic field with wall slip. Further, this study focuses on the flow dynamics of single and hybrid nanofluids through endoscopic or catheterized effects. The mathematical model consisting of continuity, linear momentum, thermal energy, and Maxwell’s equations is simplified under the assumptions of long wavelength and negligible Reynolds number. The Homotopy perturbation method (HPM) is employed to get an approximate analytical solution of nonlinear dimensionless momentum equations. Based on the mathematical relationships and graphic visualization, the influence of the pertinent parameters described the velocity profile, temperature distribution, induced magnetic field, current density distribution, wall shear stress, and heat transfer coefficient. With the help of contours, the trapping phenomenon is also presented. The results reveal that the Lorentz force significantly reduces the Cu–TiO2/blood nanofluid velocity, whereas the elevating Grashof number does the opposite. Compared with copper nanoparticles, hybrid nanoparticles have a higher wall shear stress. The increasing values of Reynolds numbers amplify the induced magnetic field on annular surfaces. In the axial direction, Lorentz force significantly decreases the current density distribution for hybrid nanofluid. Moreover, hybrid nanoparticles (Cu–TiO2) exhibit superior heat transfer than Copper (Cu) nanoparticles in the blood-based fluid. According to the graphical outcomes, hybrid nanoparticles are comparatively more effective than unitary nanoparticles in the blood.