Nonlinear four-wave-mixing (FWM) interactions enable a wide variety of photonic functionalities, including wave- length conversion, all-optical switching, signal regeneration, and generation of entangled photons. To achieve efficient FWM interactions the waves either have to be phase-matched, or a quasi-phase-matching (QPM) scheme has to be realized. However, these techniques conventionally require light-guiding media with specific characteristics. We propose a more general QPM scheme for enabling efficient FWM interactions in the presence of a large phase-mismatch. The scheme is based on increasing the distance over which there is FWM gain, while simultaneously decreasing the distance over which there is FWM loss. This is achieved by adiabatically alternating between two phase-mismatch values along the propagation path. We discuss in detail how such phase-mismatch switching (PMS) can be employed to achieve QPM of a FWM process, what the requirements are for optimal FWM efficiency, and how the scheme is impacted by nonlinear dispersion as well as optical losses. Additionally, we describe how QPM by PMS can be implemented with a silicon-on-insulator strip waveguide of which the width is adiabatically varied between two values along the propagation path. By means of numerical simulations, we show that such a waveguide can enhance the wavelength conversion by 20 dB after 1 cm compared to a corresponding constant-width waveguide. For a pump wavelength of 1550 nm, PMS enables efficient conversion (> -21 dB) around a target signal wavelength situated anywhere in the entire near-infrared wavelength domain of 1300-1900 nm.