To extract WiiWare music files, you will need to use a program called "WiiWare Decompiler." Here is a general overview of the process for extracting music files from WiiWare games:
Download and install the WiiWare Decompiler program on your computer.
Obtain a copy of the WiiWare game that you wish to extract music files from.
Use the WiiWare Decompiler to open the game's files.
Search for and locate the music files within the game's files. These files may be in the form of .brstm, .bgm, or .bns files.
Use the WiiWare Decompiler to extract the music files from the game's files and save them to your computer.
Use a audio conversion program to convert the extracted files to a more common audio format such as mp3 or wav.
What is this WiiWare Decompiler program? I can't find it anywhere online.
Also, after using ShowMiiWads to extract, the files are .bin, not any of the types you mentioned, and they don't work when opening with something like PowerISO.