How polarization effects from cations affect H-bond strength
Okay, I realized what was wrong with my picture above.

It is not the hydrogen bond that is weakened, but the OH bond within a water molecule that is weakened, and then stretches at a lower frequency.
When the cation is introduced, and is near the oxygen atom, the electron cloud in the water molecule is moved toward the cation (polarised), leading to electron density in the OH bond being reduced => weaker bond => lower frequency vibration.

The hydrogen bond is not really of interest here, although the same effect takes place when two water molecules are H-bonded. Hence, the OH stretch of an isolated water molecule will vibrate a bit faster than the OH stretch in a H-bonded water molecule.