Get it stabilized, most of what I've seen is extremely brittle otherwise, and in some cases, still so. Although the stuff I'm referring too is pretty porous, and I think is brain coral? The stuff you're showing looks different, and maybe much more mineralized, and more similar to working gem/stone material.
I think it's really beautiful material in general, and that is some of the nicest stuff I've seen. Don't see it used that often on knives, but I think it's because the sources have been somewhat inconsistent, and nobody has managed to popularize it.
If it's really dense and heavy because it's highly mineralized, it won't need to be stabilized, but I'd test a corner for durability, maybe try pinching the corner hard with pliers to see if it crumbles, or cracks. The stuff I've seen, could be easily cut with a bandsaw, but this may require a diamond saw.
