Before recombination:

1. Universe is ionized 

2 Photons put restoring force on expanding baryons                  

3. perturbations oscillate as acoustic waves.

4. Sound speed is 1.7 x 105 Km/s this is about (1/sqrt(3)) multiplied by the speed of light in vacuum.

After recombination:

1. Universe is neutral

2. Photons free-stream.

3. Sound speed falls to 3 km/s.

Such a drastic change in the velocity of sound  was addressed by Sakharov. According to his idea, modulations of the amplitudes of acoustic waves before recombination should be maintained after recombination. The reason is that because of the high speed of the sound waves, the typical wavelength of acoustic waves is nearly equal to the horizon size at the era.

Please also see pages 35 and 36 of the following article,

http://www.iac.es/congreso/isapp2012/media/Longair-lectures/Longair3.pdf

As you have mentioned velocity of sound is not directly depending on the degree of ionization of the primordial fluid. But as photons start to escape from the primordial plasma the restoring pressure falls, and the velocity of sound is proportional to the square root of (dP/d rho)S, the changes in the velocity of sound should be calculable as the pressure falls.

The exact expressions as encoded in CAMB and CMBAns is given by expression no 68, 69 of http://arxiv.org/pdf/astro-ph/9506072v1.pdf

Roughly in the radiation dominated era it goes as Tb = 2.723/a and  after decoupling it varies inversely proportional to a^2. 

Sound speed during recombination depends on wavelength. A critical barrier is the photon scattering length. Roughly: over greater wavelengths the speed of sound keeps relativistic, below it is thermal. A more detailed reply can be deduced from a (slightly dated) paper of mine: S.A. Bonometto & F. Lucchin, Astron.& Astroph. 43, 189 (1975) "Acoustic Modes and Gravitational Instabilities in the Early Universe".