I wish your photos were somewhat larger, so details could be seen more clearly.

In recent years, a LOT of coral has been characterized as "angelskin," where I would disagree with that designation. Usually this is white coral with pink spots or streaks. Actual angelskin coral is pink—sometimes with darker pink spots or streaks. Another closely-related coral comes from around the Hawaiian Islands, that is usually a more-vibrant pink with considerable variegation. Whether this is "angelskin" is a matter of opinion, I guess.

Added to the above, there are imitations that are made to resemble coral—such as dyed bone and other materials. It may take a close detailed photo to differentiate.

Think of coral (essentially gem quality coral from the Mediterranean or South China Sea) as being the "skeleton" of a marine animal. Its composition is very close to mollusk shell—being calcium carbonate. So, although it is organic, it is also essentially an organically-formed mineral. Coral will resist many normal treatments that survive whatever is harmless to calcium carbonates. However, it is attacked by some acids, such as hydrochloric acid.

It is safe to get coral wet—since it is an ocean product. It is also safe to wash coral beads in warm soapy water, and use an old toothbrush to gently release old dirt.

Nevertheless, since you are dealing with an old intact necklace, be aware that it is possible the cords (that you say may be silk) may be compromised—and would possibly break during washing. Old necklaces, strung on silk or organic fibers, should be restrung every five to ten years, if they are worn often.

This is what keeps we bead-stringers in business (!).

Good luck. Jamey