Using my own edited snippet of a song without copyright sound removal

I have recently been posting dancing videos on TikTok that I will edit using capcut. I typically play the full song and just record myself dancing.

Naturally, I just choose my favorite part of the video, and edit in the corresponding part of the song using capcut.

The issue with this, is that when I upload to TikTok, I want to use the original video's sound since it uses the exact snippet of the song I want. I am warned that the video may be muted due to copyright infringement.

If I add the sound via the in-app option, there are only specific snippets I have to choose from. Can I add the sound and just turn it down all the way while the original audio from the video plays? I really prefer not to use the in-app audio option, because it limits me to very specific sections of songs.