Smelly Feder..... Wrap?

So some years ago I bought a Regenyi feder from my instructor at the time. Since that time I've only ever had one complaint.

The wrap cord smells... BAD. Like, left in a gym bag for 10 years in the pit of doom smelly. Which consequently means after every time I touch it, my hands or gloves reek.

Short of rewrapping, which I really don't want to do because I have no problem with it whatsoever functionally, is there any way to clean this thing without damaging the tang? And has anyone else run into this problem with any other cord/leather wrap?