...not sure how gritty against the teeth can also be "waxy". If "waxy" it most likely is a plastic bead you are detecting not freshwater pearls....
Freshwater pearls...... Any pearl that is grown and marketed today, (other than those from the Persian Gulf) are considered cultured pearls. This is because these pearls would not exist without human intervention. A freshwater pearl, although it may be solid nacre, is a cultured pearl where the mussel was nucleated with a piece of mantle tissue in their mantle tissue.
All pearls cultured in saltwater are nucleated in the gonad with a piece of mantle tissue, and a mother-of-pearl bead, which is how akoya pearls are nucleated. This is why akoya pearls are cultured pearls, but they are saltwater, not freshwater, and much different in appearance and more valuable than freshwater pearls.
Anne if they feel "waxy" they are probably faux pearls. Also the amount of pearls in this sautoir indicates faux pearls. Quite in keeping. Some have a jewelled pendant or a tassel suspended at the bottom. Although usually worn from both shoulders it was often draped over only one shoulder then said to be worn "en sautoir sur l'epaule". It was popular in the 19th century. Hope this info helps a bit.