As far as I know all shagrin/shagreen is rayskin today. In the western world many years ago it was from rays, sharks, or dogfish - whichever was available. With protections and such today, rays, mostly cowrays, are the primary source. True sharkskin is finer grained and thinner than rayskin. Rayskin is also much more durable. I don't know of any suppliers who sell true shark skin shagrin. Maybe someone here will have a supplier.
Samegawa, AKA sharkskin, is the dried rawhide skin removed from cowrays, which are caught for their meat. It is covered with hard calcium nodules that protect the ray. The large bump in the middle of the hide is called the parent grain or oyatsuba, and referred to as the Emperor's node. It is the from middle of the backbone. The larger the oyatsuba, the more expensive the hide. This section is the most prized, as there is only one on each hide. It is saved for the best handles n the best swords. Dried samegawa is really hard. You won't cut it with a knife or scissors. A bandsaw with a metal blade does quite well. For trimming the seam along the ura once wrapped and dried on the tsuka, use a fine tooth rotary sawblade in a Dremel. A 1/2" to 3/4" round blade is best.
Traditionally, one entire hide was used for the tsuka. The dried rawhide was soaked until pliable, trimmed to the approximate needed size, wrapped around the wooden tsuka core, bound tightly with twine, and allowed to dry for about a week. The oyatsuba is always placed in the center of the omote (show) side. Once dry, the hide was trimmed to meet perfectly along the ura (backside) of the tsuka. After assuring a perfect fit, it was glued on with rice glue, bound with twine again, and allowed to fully dry. Some of these tsuka have lasted hundreds of years and are still holding tight.
The rest of the hide was used for saya covering or the grip area near the koiguchi, and decorative other things.
When wartime came, the supply of samegawa was not sufficient to wrap one per handle, so the hide was cut into strips called panels. A panel was glued on each side. This allowed many tsuka to be made from one hide. The most valuable one had the oyatsuba, and was saved for an officer. The difference in cost of a panel with the node vs a plain one can be triple or more.
While samegawa is the preferred wrap for a Japanese sword, many other skins and leathers have been used on sword handles. I have used elephant rawhide as the wrap on a tsuka. It looks like fine grain grey samegawa. It is dang near as hard, too.
If you want the samegawa to be other than white, it can be lacquered with a good grade hard lacquer. Urishi is the preferred type, but expensive and many people are allergic to it. Furniture grade lacquer works fine. The lacquer is usually lightly sanded after drying to expose white dots on the raised areas and the color in the recesses. After sanding, hand buff and wax and tsuka to get a good polish.
The soft rayskin that is available in many colors has been vegetable tanned and sanded to be thin and pliable. It is used for wallets, belts, and insert pieces on sheaths by leathercrafters, and sometimes for clothing like vests. It isn't the traditional material for wrapping a tsuka, but certainly can be used. It is generally from smaller rays of many species. Many of these soft skins have a fake oyatsuba glued in the center.
Fun trivia fact for sword nerds:
The rays that make samegawa are not found in any quantity around Japan. The old tsukaishi had to import it from China and India.