Ok, I installed patch 1.01, and it seems to have done the trick; at least I could now play three missions without the game crashing. Why didn't I look for a patch in the first place? Probably because I thought GOG had supplied the patched version.
Anyway, patching the game apparently creates some sort of checksum problem, because thereafter it demands a CD and refuses to start otherwise. There are, of course, ways around that problem, but for obvious reasons I won't post a link to them. ;-)
So, in short:
1. Patch it to 1.01
http://www.fileplanet.com/64352/60000/fileinfo/Desperados:-Wanted-Dead-or-Alive-v1.01-Patch 2. Apply semilegal measures
3. Profit
Worked for me, thought it would be nice if GOG would patch this version of Desperados, so we won't need to crack it.
EDIT: Scratch that. 4 Missions without a hitch, next mission the sound bug rears it's ugly head again. Damn. I hope somebody takes a look at this...