You can play AIFF files with a Mac Classic with a very small application (10K !) called "SFplay" ©1991 by Reinder Verlinde.

The user interface is minimalist. Just double-clic on the file to play it (the application doesn't have any "Open..." command).

With ResEdit, change the type of the audio document you want to play to "AIFF" and the creator to "®√PL".

Here is a link to download it : http://bit.ly/17vXpPR

The music is playing in the background, allowing you to work with another application in the same time.

I used this application on a Mac LC with sytem 7.0.1, without QuickTime, so it should work with a Classic.

The files i used to play were 22 or 11 kHz 8 bits mono sound file.