Seat Belt Cleaning

I am in the middle of getting my 1971 Demon 340 restored. In the twenty years it sat, a lot of stuff got real dirty. The armrests were starting to get hard as a rock. I cleaned them and got them softened up again using Murphy's Oil Soap. But now I need to know what is a safe way to clean the seat belts. Thank you in advance for the suggestions. Merry Christmas everyone.