Hi Lily,
I hate to tell you this, but unless you have the original Miki clasp (stamped), you cannot prove provenance.
The clasp and the original papers are the only things left that can give the pearls a better than average valuation; lose them, and you will end up with fair market value for non-branded pearls.
Knotty is very correct in her ascertation of the different values applied to your necklace... if you want to go through professional channels, then stick with the estate jeweler (after getting an independent estimate on the current Wholesale Value of the piece by an appraiser that really knows pearls- this will cost you approximately $200-).
Ultimately, you will probably be able to get a better price through a private sale. Good luck!