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A hypervelocity imperfect gas nozzle with a shared wave-elimination contour is designed by the residual correction method, allowing the test Mach number to be varied by changing the throat contours. Owing to imperfect gas effects, the nozzle designed by the classical method of characteristics with boundary layer correction does not produce a uniform flow field, resulting in significant deviation from the target Mach number. In this work, the computational fluid dynamics solver is used as an independent module without being coupled to the optimization code, reducing the design complexity. Designers can choose the appropriate solver according to the specified physical characteristics to consider imperfect gas effects. The Mach 15 hypervelocity nozzle designed by the residual correction method better eliminates the Mach waves and achieves a much higher flow uniformity than the nozzle designed by the classical method. On this basis, the dependence domain of the shared wave-elimination contour and the influence domain of the transonic solution are solved by the method of characteristics, and a replaceable throat contour is rigorously designed from aerodynamics theory. Quantitative evaluations show that the nozzles with a shared wave-elimination contour have the same level of flow uniformity, achieving high flow quality at Mach 13–15. The evaluation results validate the design's feasibility, supporting the future construction of hypervelocity tunnels.