Very Old Pearls

I inherited a double-strand of pearls with a 18 carat gold clasp. They belonged to my great-great grandmother and are well over 100 years old. They are about 6 mm diameter and not perfectly round, each one different, but one has to look at them closely to notice it.

The string is intact but quite dirty.
Am I right to assume they are natural pearls? Would having them cleaned and re-strung (they are not very clean anymore) devaluate them? Thanks.