Hyperbolic shear polaritons (HShPs) emerge with widespread attention as a class of polariton modes with broken symmetry due to shear lattices. We find a mechanism of generating quasi-HShPs(q-HShPs). When utilizing vortex waves as excitation sources of hyperbolic materials without off-diagonal elements, q-HShPs will appear. In addition, these asymmetric q-HShPs can be recovered as symmetric modes away from the source, with a critical transition mode between the left-skewed and right-skewed q-HShPs, via tuning the magnitude of the off-diagonal imaginary component and controlling the topological charge of the vortex source. It is worth mentioning that we explore the influence of parity of topological charges on the field distribution and demonstrate these exotic phenomena from numerical and analytical perspectives. Our results will promote opportunities for both q-HShPs and vortex waves, widening the horizon for various hyperbolic materials based on vortex sources and offering a degree of freedom to control various kinds of polaritons.