Speed of light, frequency, and wavelength are the three quantities that are so related that it is hard to tell them apart. What if changing c changes lambda but not nu?
The inverse is easier to picture. If you just imagine the cosine wave suddenly shooting along faster, then lambda stays the same but nu rises. If the waveform slows down, lambda again is constant but nu falls. I don't see lambda changing with c unless you also play with something else.
If (as we think has happened) space stretches out while the photon is in flight, lambda goes up as nu goes down but c need not have changed at all.