I am using grape vines in my pygmy cages and have had no trouble with them molding, except for a little mold occasionaly at the bottom where they vines are in the dirt. Any of the vines not touching dirt have no mold.
A mix of 1 part bleach to 10 parts warter and soak the vines works. Soak them for a little bit, then wash well. I repeat the rinsing with regular water several times.
Another method I have used is to cook the vines in the oven. I am not sure of the exact temperature, but a search should return the temperature. I like this method as no chemicals are involved. You just have to be careful not to burn the vines on any of the burners etc.