The Mikimotos are very pretty. Such lovely overtone colors! It's a fantastic thing to inherit, congratulations.
How long is the necklace? I count 50 pearls, not graduated. Have you measured their diameter with a mm ruler? We can estimate their size if we know the length of the strand (include the clasp).
I hope you will decide to wear them! It is probably a good idea to have them restrung, as silk deteriorates and weakens over time with wear, and if it broke you could lose the necklace. If the silk is at all stretched out (if there is any gapping in the knots), that is an indication they should be restrung. If the knots all seem tight and clean, maybe your grandmother had them restrung in recent years -- or didn't wear them.
Are those loose pearls in front? If you would like us to comment on them, please photograph them close up on a white paper towel. From here they look like akoyas also.