It is a dj mix so all recordings should be unique.
This is because the mixing process will usually have parts of the next and previous song and possibly other samples added for effect so this recording will be different than the normal version.
The work should normally be the same with a remix as in the original as the sing itself is the same as the lyrics and the tune will be similar if someone does a cover.
There is a recording to recording relationship that you can use to indicate that this remix was used in the DJ mix.
You can also credit the person that performed the remixing of the track.