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Stellar coronal mass ejections (CMEs) from host stars are an important factor that affects the habitability of exoplanets. Although their solar counterparts have been well observed for decades, it is still very difficult to find solid evidence of stellar CMEs. Using the spectral line profile asymmetry caused by the Doppler shift of erupting plasma, several stellar CME candidates have been identified from spectral lines formed at chromospheric or transition region temperatures of the stars. However, a successful detection of stellar CME signals based on the profile asymmetries of coronal lines is still lacking. It is unclear whether we can detect such signals. Here we construct an analytical model for CMEs on solar-type stars and derive an expression of stellar extreme-ultraviolet (EUV) line profiles during CME eruptions. For different instrumental parameters, exposure times, CME propagation directions, and stellar activity levels, we synthesized the corresponding line profiles of Fe ix λ 171.07 and Fe xv λ 284.16. Further investigations provide constraints on the instrumental requirements for successful detection and characterization of stellar CMEs. Our results show that it is possible to detect stellar CME signals and infer their velocities based on spectral profile asymmetries using an EUV spectrometer with a moderate spectral resolution and signal-to-noise ratio. Our work provides important references for the design of future EUV spectrometers for stellar CME detection and the development of observation strategies.