VirtualDubMod (freeware) will allow you to remove the existing audio from the AVI and add in the new audio and save it as a new AVI file.
Information & Download:CODE
http://www.videohelp.com/tools/VirtualdubMOD
...and I also found this while looking for it, you may find it useful:
QUOTE
Replacing Audio Streams With VDM:
With VirtualDub Mod, open your video. Then go the 'Streams>Stream list'. L click on your audio file and then select 'Disable' to the lower right.
Then L click 'Add' at the top, select your new audio track, open it, then OK and you are done.