Looks like a coticule to me, but your photography is not great.

I have never heard of a light colored German hone.

The German hones I have had in my possession have all been very solid, heavy even but soft, claylike, unlikely to chip, more likely to dent.

The coticule is more brittle, harder, likely to chip, more abrasive, less clinging. But still not a tough stone.

Without using it, I can not help anymore.

We really need a test of specific gravity or something for these unusual finds.

Was the green, an oil that had been used that you sanded out of the surface except for the dished edge?