Sequel to the existence of dual solutions of many boundary value problems and inevitable dynamics of ethylene glycol, nothing is known on the stability analysis of such base fluid conveying copper and titania nanoparticles on a stretchable/shrinkable curved object. The composite nanoparticles in hybrid nanofluids improve the heat transfer characteristics by boosting the thermal conductivity. The effects of non-linear radiation and heat source/sink parameters are also incorporated. Stability analysis is performed to check the existence of dual solutions. A built-in technique in Matlab, namely bvp4c is used to solve the governing equations numerically. For both hybrid and nanofluids, the effects of shrinking and suction parameters on the coefficient of skin friction and Nusselt number are studied. This study highlights the importance of these nanocomposites; as copper increases porosity and titania acts as a photocatalyst. The values of the coefficient of skin friction for the upper branch boost over a certain range of shrinking parameters; however, the reverse pattern is found for the lower branch. The radiation parameter has no consequence on the boundary layer separation, but it contributes to enhancing the heat transfer rate. Furthermore, a comparison is made with past findings, which indicates that the current results are in good conformity.