You don't have to do it with a wad. It's a better idea to do it with a pk3 (zip) file anyway, because it will compress the files. Also, no need for SLumpEd or XWE. See the wiki: Using_ZIPs_as_WAD_replacement
It's possible to do it without renaming the files if you use MAPINFO to explicitly assign the music to maps, but that's your call. If you're just trying to replace the original music, it's sufficient to just rename things.