Unfortunately, with the music that's a lot easier said than done. I've never figured out how to properly export PICO-8 music, and the sounds used for music are a bit... less-than-organized because I never wound up having to clear out unused bits. I also use a reverb effect that's enabled by modifying a bit of cart memory, so I have no idea if that can be used with the export feature.
That said, if you've got PICO-8 and are feeling up to sifting through it, the music and sounds are all readily accessible in the PICO-8 cart.
(Or if you just want to listen you could technically just leave the executable running, since there's no idle sound effects.)