When two billiard balls collide in normal situation (on earth) we hear the sound due to their impact. This is a sufficient proof that the collision is inelastic in nature due to loss of energy in the form of sound. But suppose the same collision occured in space, then we will not be able to hear the sound due to collision as there is no medium for sound to propagate. Then can we say in this case that the collsion is elastic since no energy is dissipated? (We assume that the balls do not deform during the collision)
The sound you hear comes from ball's deformation, albeit very small. Vacuum or not doesn't matter here.
Strictly speaking, there are no elastic collisions in macroscopic world, some part of energy is always converted to internal energy of atoms/molecules, i.e., is dissipated. But if that part is negligible compared to total energy of the balls, you can assume that collision is elastic.
The dynamics of a collision is very complex but when trying to predict what will happen after a collision simplifications (assumptions) are made to allow the analysis to be done.
Often this leads to a result which is accurate enough and such an example of "billiard ball dynamics".
In such a collision it is assumed that the time during which the collision takes place is much less than the time scale for the complete motion of the billiard balls, the collisions are elastic ie kinetic energy is conserved, which in your example means that the loss of energy due to sound waves being produced is much less than the total kinetic energy of the system of billirad balls, etc.
The sound from a collision of billiard balls comes from the compression of the air between the billiard balls and the billiard balls actually vibration due to compression pulse produced as a result of the collision passing through them.
These pulses make the surfaces of the billiard balls move which in turn make the air around the billiard balls move.
Also in their passage though the billiard balls the compression pulses make the billiard ball atoms vibrate more with the effect that the temperature of the billiard balls rises ie there is a change of some of the kinetic energy of the billiard balls to heat.
Again the assumption is made that this conversion is very small - the collision is elastic.
With no air around the billiard balls no sound waves are produced so the approximation that the collision is slightly better.
To illustrate the complex nature of a collision I could not find a super slow motion video for a billiard ball collision so have a look at what happens to a golf ball hitting a steel plate.
How much translational kinetic energy the golf ball loses to the vibrations of the golf ball (and the steel plate) could be found by measuring the speed of the golf ball before and after the collision although after the collision identifying where the centre of the golf ball is might be a little difficult.