Alright. Thanks to what jurassicPieter and others from this thread said about muting the sound effects I was able to mute the sound effects and record the part of the song I was looking for. I used the Steinberg UR22 that I have to record it from my wii, and I used Nintendont to play the iso without sound effects on the wii.
I noticed that when Zant's Hand is approaching Link, the extra bit of music that plays on top of the Palace of Twilight Interior music actually doesn't have two volumes that it plays at when the hand is a certain distance from Link. Once the music starts, it keeps increasing in volume as the hand gets closer to Link then when it gets really close the music just plays at the max volume. I decided to record this part then edit it into PrimeBlue's flac rip that I have. I thought it would sound better there instead of being its own individual track. The part where you first hear Zant's Hand nearby is at about 3:00 in this file and I think it reaches its max volume at about 3:18. If anyone else wants this I uploaded it here: https://mega.nz/file/vk1kFB5A#z4Of6ktXpyWhEoWMgcB1QkAZKT6NiQ02tNILy4sLkBc
If anyone is interested and gets a chance to listen to this can you please let me know how you think what I did sounds? When I listen to it myself, I don't notice any clicks where I ended PrimeBlue's track and pasted my own. I pasted mine at 2:56.283 in PrimeBlue's original flac file if you want to listen closely yourself. The swishing sound that plays at that time is supposed to be there and that's in PrimeBlue's original file, too. Just a heads up, the fadeout I used sounds different from the other tracks in his rip because I didn't know how to match the one he used.
If anyone wants a version of this on its own (a version not mixed into PrimeBlue's track) or maybe one that loops twice let me know and I'll try to record it. Also, if for whatever reason someone could use the game save that I used for this let me know and I'll share it. Some parts of the game might be stuck however because I used cheat codes to speed up getting to the Palace of Twilight and I skipped many things in the game.