I think if you change the names of the MP3s to match the present ones that will work.
However I have played MP3s while running Civ. With XP anyway. I was using Music Match Jukebox but that requires a lot of memory because Music Match is a hog.
I think if you turn off the music but leave the sound effects on that will do the trick. That is what I did anyway. Playing a CD would use up less CPU cycles though. So if you have two CD drives you could have Civ III in one and an audio CD in the other.
I now play with sound effects only. That way the game has more CPU cycles to work with and PIII 700 needs all it can get with Civ III.
It may also be that you sound card simply can't handle that many digital audio streams.