There needs no acceleration. Just a closing or opening speed of the objects in question. Also, you are correct that we see these shifts due to the wave length change. This is also has an effect on the spacings of the photons (which are the same thing).
Photons emitted at a set interval expand out in a perfectly spherical pattern and if the light source is in motion the spacing between the surface of these spheres are not the same distance all they way around. (hence doppler shift).