Hello,
My name is Pedro, I'm a music producer from Ecuador.
I can mix the songs in a similar way and do the swap you need, nevertheless, it is important to notice that I would use the official recordings of those songs and mix them, instead of producing the whole mix out from the start (like the music in the video). I mean, the music in the video is sang by the same artist and produced out from the start (drums, pianos, etc.). So the result would be different, since will be just mixing different songs, though I think It would also work.
I don't know all the songs in the video, so I would need you to provide me links to the songs (Like YouTube links, so I can extract the audio).
Best,
Pedro C.