You can just convert an MKV to an MP4 without re-encoding the video:
https://stackoverflow.com/questions/28441946/lossless-conversion-of-mkv-to-mp4-with-handbrakeThanks. I already did it with Handbrake. 😃
Does the PS4 support the HEVC/H.265 video codec? Still has to be in the proper file container anyway.