If we introduce a uniform electric field throughout the double slit setup and along the slit to screen straight path, how will it affect the wave nature of the particles?
I don't know, but having a magnetic field between the two paths changes the phase difference between them, and so must change the wavelengths along the two paths. See the Aharanov-Bohm effect. The voltage (scalar potential) appears in those equations.
Whatever it does, electrons will still behave as both waves and particles.