Yah most certainly don't have to convert to .WAV
A CD burner will use the CDA file format, and that will work. But for old CD players, they won't play "data CD's" and when you stick a bunch of mp3's on a CD - that's a "data CD".
So you either need to burn an audio CD, or upgrade to a multi-read CD player.
Yah can use media player to burn an AUDIO Cd. It'll take MP3 files in a playlist then write audio tracks that a regular CD player can handle (.CDA format). assuming, of course, your cd player doesn't balk at the media!!!