Might be tricky.
Most older consoles used sequenced music (think midi or tracker software) as opposed to wave (mp3 files for one) and while the N64 had options for streaming stuff most was still more in the sequenced realms. Converting wave to midi is kind of possible with some modern tools that will do an analysis and try to fit it to whatever instrument bank you feed it but results of such things are usually less than stellar.
If you can make a sequenced version of your audio there are a few tools, however I am not familiar with the specifics of them or what the kids are currently favouring.
Still
http://www.romhacking.net/utilities/589/ ,
https://github.com/sauraen/seq64 ,
https://www.smwcentral.net/?p=viewthread&t=87337 and
https://www.smwcentral.net/?p=section&s=sm64music are some things to get you started there.
Some people will make hacks to force games to play back (there are various such things for the DS New Super Mario Brothers, and I think I saw one for Mario Kart a while back) streamed stuff if you must use that. You would also come the other way and make an emulator only hack that triggers an external audio player at a suitable time. I don't think you will have much option here to abuse the sample banks to put samples of each part of the song in said samples and play them back one after the other.
The first option is not what you might call a typical hack either, and will likely be quite involved compared to the text/levels/graphics fiddling most newer hackers find themselves doing here. On the other hand mario 64 has been disassembled and documented fairly well (same links as above will find various documents and details on that one) so you do at least have that.