Other things to watch for:

Ivory (and bone) will often still have visible saw marks on the insides of the scales. Even if you can't tell bone from ivory, that will at the least rule out synthetics.

I've never seen a celluloid (or other synthetic) handle with a metal wedge, yet the vast majority of ivory handles have metal wedges. I've only come across one razor dressed in ivory that had a synthetic wedge. Bone is more of a toss up - usually 20th century examples have synthetic wedges, but prior to 1880 had wedges of metal, horn, or even more bone.