I inherited my GGF's Coticule, back then it was darkened and water would just bead off, posting pictures of it on the forum I was told the stone was probably heavily used with oil.
I lapped it and it cleaned it right up, looking back now I wish I hadn't done that and wish I had left it as original as possible, ah well.
So even if you really worry, a quick lapping will take care of it.
I've seen pretty old Coticules that came with hand written notes from owners / users that said to use it with oil, or 'vaseline oil' in a french written note
Here's one that came with a Coticule, says in french to use it with oil and only use the weight of the razor, no added pressure
Attachment 279062