The reason why the music cuts out is because of the piranha plant nearby. Normally when you walk close to a sleeping piranha plant, the music fades out, and the lullaby music plays instead. When Mario walks far enough away, the music turns back to normal.
The reason that the music fades out completely for cannonless is because of the downwarp after collecting the star. When Mario grabs the ledge to collect the star, he is still in range of the sleeping piranha plant's lullaby. After the downwarp the game recognizes Mario significantly out of range of the piranha plant, so the game cuts off the lullaby at the same time that it would normally start playing the music for the course. Due to this, any music that tries to load is cutoff, and we can only hear Mario speaking.
To verify, try killing the piranha plant then doing the cannonless setup vs just doing the cannonless setup when leaving it alive. The music will only cutoff when the piranha plant is alive.
SM64 is actually pretty stable in the crashing regard. As far as I'm aware, there's only one specific reproducible crash due to a null read when looking for sound. This is the infamous sound glitch in SSL, where the game essentially tries to play too many sounds at once, glitches out, and stops playing any sound at all. This sound glitch was patched out in the US release anyways, and is only possible on the J 1.0 release of SM64.
If you want to know the answer to similar questions to this one, I'd recommend checking out the SM64 TASing Discord where people analyze and TAS the game.