Type I X-ray bursts (XRBs) are powered by thermonuclear burning on proton-rich unstable nuclides. The construction of burst models with accurate knowledge of nuclear physics is required to properly interpret burst observations. Numerous studies that have investigated the sensitivities of burst models to nuclear inputs have commonly extracted the strength of the NiCu cycle in the rp process, determined by the Cu-59(p,alpha)Ni-56 and Cu-59(p,gamma)Zn-60 thermonuclear reaction rates, as critical in the determination of reaction flow in the burst. In this study, the strength of the cycle at the XRB temperature range was estimated based on published experimental data. The nuclear properties of the compound nucleus Zn-60 were evaluated for the Cu-59(p,alpha)Ni-56 and Cu-59(p,gamma)Zn-60 reaction rate calculations. Monte Carlo rate calculations were conducted to include the large uncertainties of nuclear properties in the calculations. In the current work, a weak NiCu cycle is expected, whereas the rates adopted by the previous studies suggest a strong NiCu cycle. Model simulations were performed with the new rates to assess the impact on Type I XRBs. The results show that the estimated cycle strength does not strongly influence the model predictions of the burst light curve or synthesized abundances.