Thanks for the interesting replies!
I didn't know it was still possible to get hold of carbon tetrachloride, Steve. I think aggressive solvents are supposed to be bad for leather, since they can wash out the natural oils, but it might be worth further enquiries. I also didn't know copper sulphate was a fungicide, but I see from searches that it is used in 'Bordeaux mixture' to control fungus on grape vines.
I had hoped to find something that does not involve soaking the leather in liquid, and the last two suggestions might well do the trick. Thymol looks extremely interesting and not difficult to get hold of. It seems to be pretty harmless ("an active ingredient in food flavorings, perfumes, cosmetics and mouthwash"), and apparently the crystals evaporate slowly, so if I just put the case in a sealed container with some Thymol it might well do the job.