Convert 96 Khz to 48 Khz audio: is this simple downsampling method ok?
Since you have already properly low pass filtered the signal, then there is no risk in taking every other sample to complete the downsampling operation.  If you were to create a low pass filter that passed your spectrum of interest with no distortion, and rejected all energy in the alias frequency locations then taking every other sample would provide a perfect downsampling by a factor of 2 (there would be no distortion in you signal of interest). Of course, such a perfect filter is not feasible to implement but stated as such to show that the issue is not in taking every other sample but entirely in the filter design itself.